Can You Pass Harvard's Entrance Exam?

[@prithvichidri9634]

For the guys who directly substituted x= -2🤙

[@ernesthakey3396]

Yep - math nerd with an MIT degree, just looking at it I figured X needs to be negative so that it turns into an addition, -1 doesn't work, -2 does, done. Of course for an exam question they probably require you to show your work, and you don't get credit for just saying "It is intuitively obvious!"

[@vvTejedor]

Yes, but youcan say, that according to Vieta's formulas if there is a rational root, 12 can be divided to it.

[@kutenor]

In my head in -2^3 seconds.

[@arturkowalski5151]

5 seconds for me. And I have studied history, not mathematic...

[@AasimSyedGPlus]

But that's not the only solution

[@tom-kz9pb]

Seeing -2 only took about 2 seconds. For Harvard, you should need to find the complex solution, as well.

[@potrahsel4195]

Not sure about that.

[@AllDogsAreGoodDogs]

Wolfram came up with x=-2 under "real" solutions. I agree with @potrahsel4195 .

[@chrisclub3185]

Just divide the poly by x + 1 then use the quadratic formula on the resulting quadratic. If this is what’s required to get into Harvard, Harvard has fallen deeply

[@chrisj5443]

Then it should be a harder problem. I'm dumb. It took me 5 seconds.

[@suhumm]

​@@chrisclub3185 by x+2, not by x+1 ))

[@lefantomer]

If you can't and you still want to go to Harvard, go over to the Admissions Office and plunk down a few thou$and -- much much less than for admission to the college as a full daytime live-in student -- and sign up for Extension School. That's the night school. Pick your concentration if you want a degree. You will attend classes at night run by full professors (unless they've changed the policy), will have to do class work and term papers and a thesis like everyone else, attend Commencement and get a Harvard degree for a fraction of what you would have had to pay had you been "accepted".

[@johs9000]

Solved that in a micro second. You clealy need x^3 to be negative, then it follows.

[@TooTallForPony]

Not just negative, you need x < -1 for this to work. If -1

[@robertfitzjohn4755]

I found x = -2 pretty quickly, but as it's a cubic equation it must have three roots. Surely to get into Harvard you have to do better than just say "oh, the other roots are complex, so I won't bother with them"? (Unless they specifically asked for only real roots, of course.) After a bit of work I managed to find the complex roots, and substitute them back into the original equation to prove they were correct. Then again, I did sit the Mathematics entrance exam for Natural Science at Oxford, some decades ago.

[@TonalWorks]

Yeah, that was a wierd assumption indeed.

[@lefterismagkoutas4430]

it's not that hard to find the complex solutions in the state that he left it, hell in most college classes they will leave it like that because it is almost implied.

[@algorithminc.8850]

I look forward to checking out your channel. Subscribed. Thanks. Cheers

[@higher_mathematics]

Thank You Mister. Have a great day!

[@TheOldeCrowe]

1. kind of easy to see thar x² - x³ = 12 when x = - 2. 2. synthetic division then gives x³ - x² + 12 = (x + 2)(x² - 3x + 6) 3. the quadratic formula gives the two additional complex roots x = ½(3 ± sqrt(9 - 24) = ½(3 ± sqrt(15)i).

[@christianeb8494]

Tout simplement.

[@benyseus6325]

Those who just used the cubic equation and were done with it 🧠 🗿

[@kumertd]

Gosh, what does higher mathematics mean in 2024..?

[@cookiemonster-nk3xb]

Do you want a fresh one..mind your manners. If you want hard problems go to Presh Tell Walker at Mind Your Decisions 😂

[@maxblatter]

Sorry, but as an engineer, I just had to think of the following joke: Two balloonists have lost their way, when they see a man on the ground underneath their position. They shout: "Where are we?" No answer. After a while - they are nearly out of earshot: "You are in the balloon basket!" - One of the balloonists sais to the other: "He must be a mathematician." - "What makes you think so?" - "Look: First, it took him a long time to find the answer. Second, the answer was correct. Third, the answer is of no use!" By the way ... I passed all exams (also in mathematics) with no problems. Not at Harvard, but at the Swiss Federal Institute of Technology...

[@wisemang73]

Passes harvard math exam. Fails 1st grade writing

[@gabbleratchet1890]

It's not really the entrance exam for Harvard. There is no such thing. They look at your grades and SAT/ACT scores.

[@NainoLoL]

​@@gabbleratchet1890 Or alternatively, your wallet 💰

[@jayrussell3796]

​@@mxm5783I actually commented that 2 days after your post...that scribble drove me crazy😅😅

[@robertveith6383]

Original poster, you failed First Grade Writing by not writing sentences.

[@gaynzz6841]

@@gabbleratchet1890 No, they look at your bank statements.

[@andytraiger4079]

Inspection reveals X must be a negative number for a real solution... and a very small negative number because X^3 blows up faster than x^2.

[@bartermens8219]

You also draw 2 graphs x² ans -x³. And see where they are 12 apart. Sounds much easier than all the hokus pokus with x.

[@vict85]

x² - x³ is negative for x > -1, and the function is monotonically decreasing. Therefore, the function has a single negative real root. It is trivial to identify -2 as the real root. The complex root requires a polynomial division. Obviously, there exists a closed formula for the roots of any cubic polynomials, so...

[@udhessi3444]

7.27 minutes for an incomplete solution ! It should go like this : -2 is an obvious solution, so divide x3-x2+12 by x+2, that's x2-3x+6, which you simply solve with the quadratic formula, hence two more roots [3+i.sqrt(15)]/2 and [3-i.sqrt(15)]/2.

[@steveruschin5191]

I’m useless at math, but it took me 2 attempts at negative numbers in my head and no more than 20 seconds to get it right. But it was just a guess

[@superserioes]

I was very bad at math at a normal school. Of course I wouldn’t have passed this test. But I’m positively surprised that not only did I guess -2 fairly quickly, but I also completely understood the proper solution here. For me that’s something, considering this is effing Harvard.

[@gaynzz6841]

You still wouldn't go to Harvard.

[@superserioes]

@@gaynzz6841 You don’t say

[@damiank6566]

Finding these "complex roots" is a classic square function problem. It's a high school level math, not a rocket science

[@killianlomax8237]

Do a readable, well-written, straight X ... how hard can it be??

[@AbrasiveTea]

I don’t know why this was a hard problem. I knew it was a negative because of the exponents and the subtraction so I just went through the squares added to cubes that would get me 12 and got there quickly

[@bsharpmajorscale]

I actually tried a fractional answer at first, but then I remembered that odd powers change signs. Can't say as I'd have figured a complex answer except that Wolfram Alpha listed one when I checked my solution. Neat.

[@bartoszwroblewski8285]

This is how economy is explained. Then no wonder, that musicians do much better in business, than economists :-)

[@jasonbarker1587]

I love Harvard, but the MIT in me found the answer in a quarter of the time.

[@Achrononmaster]

I like the problem because I'm a bit of a nerd. But I would never administer it as part of an entrance exam if I ran the university department. It tells me nothing useful about the prospective student. I would rather know if they can _learn_ mathematics --- slowly as they like --- but _learn a lot_ nonetheless, and then also what they'd like to do with the skills (say, aspiring to not start world war III, but rather do the opposite).

[@Achrononmaster]

I think there is a satisfactory way to learn this about a prospective student, though it might take up more of my time, or for mass entrance exams it might take more time to read the exam output. But so what? I get a better student filter.

[@Achrononmaster]

For all the eyeball x=−2 bros 🤘below: if Harvard is a place of wisdom that'd be a fail, if the point of the entrance exam being to demonstrate specific technical skill in short span of time, so it is marked as a "show some damn complicated working" question, not a "get the correct answer" question. Not saying that Harvard admins would be so wise. But even then, it is a stupid entrance exam question, since it tells me nothing about how good the examinee is at _learning,_ which is really the info I _want_ to know.

[@Dr_DeeDee]

I figured that out in my head in about 30 seconds

[@tekniq30617]

Why every time he said "you can simply write it like this", it got more complicated

[@analogman9697]

He didn't tell you that this is the math component for the Art School exam.

[@hstrinzel]

Congratulations to Harvey's University. Home of the Big Harvey's Burger in Canada!

[@tesmith47]

where the hell did this guy learn to write X?????????

[@arekkrolak6320]

Since this is cubic it must have a trivial root since no high school teacher knows how to solve cubic :)

[@Jonasjonkable]

The entry level to pre school is learn how to write X

[@gaynzz6841]

I don't need to pass the exam if my parents have enough money.

[@leighvaughton2740]

Yes, I have 3 million to gift Harvard.

[@unknowneditz108]

Bro, this is no harward question any 9th class student in india could solve it.

[@r.markclayton4821]

Does Harvard have a high school?

[@PlumbuM871]

I figured out the answer in my head in 10 seconds. Is this a problem from Harvard? 😂

[@utube1818]

Harvard Michegan, not Harvard Massachusetts

[@andreward8510]

its the time pressure during the exam that matters, not the complexity of exercises.

[@Al-Capone]

Если это задача из вступительного в Гарвард, то понятно почему такой низкий уровень образования в США и ЕС.

[@popgoesaweasle920]

Thank god there are people that can do this else we would still be wearing fig leaves over our genitals. Utmost respect to the science community.

[@RadenVijaya]

That is a junior high school level problem 😅

[@Steve_K2]

I got lost at the formula in the box. Can someone tell us the practical value of this knowledge?

[@williampankratz600]

Even high school algebra can solve that problem

[@geoplaten337]

I’m betting very few Hard students could solve this. They’re too busy social justicing….

[@ahmadquraan5623]

-2 simple ,didn't even try to use paper......

[@SSN515]

I be black. I demand a DEI admission. I don't need no stinking math. I be going to lawyer school and getting into politics.

[@markjones5268]

The correct answer is: My parent’s just donated $5M to the school.

[@aliahmed800]

😅

[@AakashSharma-le8pm]

You have to pass the school as well. Donation can only get you admission. ​@@aliahmed800

[@gaynzz6841]

Yup

[@orsolyadr.szepesi8615]

😂😂

[@divermike8943]

@@markjones5268 LOL!

[@wolfhard2420]

Brings me back to Highschool, when the math teacher filled the blackboard with lots of mystery and lacks of explanation skills, so we understood nothing

[@davidb9562]

But this guy "explained" too much during most of the video (extremely tedious) and then rushed it at the end. Big fail.

[@user-tk1ih4zr2s]

just like my teachers, they memorized it but didn't understand it and therefore could only repeat it but not explain it.

[@VaraLaFey]

That is ALL math "teachers" I have EVER seen. They like to show how smart they are, so they restate problems unnecessarily, and suddenly we're not sure what happened. So we try to figure it out - and now we've fallen behind. Which is part of why I, who was skipped a grade in school, have nonetheless been a math-cripple my entire life. That said, I was almost able to solve the initial problem in my head. I suspected x = -2, but in the very last step forgot that 4 - (-8) is 12 instead of -12. Oh well. I'd never get even that far on a more complex problem.

[@creounity]

Why wasn't she explaining enough? That is her direct obligation to do this!

[@CalvinNHobbes1985]

It was pretty clear. Just say your bad at math instead of blaming others for your lack of intelligence

[@daniellemb1592]

I am very bad at maths, and had always been. I watched at x² - x³ = 12 and thought "x has to be negative, let's try with -2", so I calculated mentally and wrote 4+8=12. Seemed good ! So x= -2 Don't ask for the demonstration ! 😃

[@gerardsmadja1323]

seems obvious , x==2(1-x0 = 12. x should be an integer, and the only factors that can be considered with one of them a perfect square are 4 and 3 so 1 - x = 3 and x = -2

[@rvqx]

@@gerardsmadja1323 Correct, first find one solution and then divide the cubic equation by x minus that solution. So then you must (-x³ +x²-12) divide by (x+2) and that gives you x²-3x+6 which gives you the 2 complex roots. That`s the common way to solve a cubic equation in the math world. In normal world you use a calculator.

[@gerardsmadja1323]

@@rvqx Perfectly right. I assumed wrongly that the iinteger result was the one xpected.

[@steveperry1344]

that's what i came up with also, just a shorter way of doing it and no pencil and paper. i haven't done math in over 50 yearsand only got as far as algerbra ll in high school.

[@einherz]

same. exactly same:)

[@divermike8943]

Oh ! He didn't calculate the Complex root! That's not the Harvard Way! The roots are X=-2, X= (3 +sqrt (15) i) / 2, X=(3-sqrt(15) i) /2

[@JimmyD806]

But completing the square would have been a whole other page of math. LOL

[@RexxSchneider]

@@JimmyD806 ... and using the quadratic formula would take maybe two more lines. Worth it to get all three solutions.

[@ericanthonyjones2131]

like finding the three cube roots of 1. including the two complex roots

[@PaxAlotin-j6r]

The Harvard way is simple --- if you have the money -- we will accept your answer - no matter how wrong ---

[@arghyanildey7563]

Here is your admission letter from Harvard. Now give us dollars

[@ila9063]

There is no entrance examination for Harvard University.

[@Cotronixco]

Yup. If there were, nobody would attend.

[@q-tuber7034]

There is a strange poetry in how the bizarre way of writing the letter “x” (completely missing the essence of the x) is echoed in the bizarre, overly complicated way of solving the problem

[@geirbalderson9697]

How about more confusion as the back to back 'C' kept distracting me! Why not plain old X????

[@Humanity101-zp4sq]

@@geirbalderson9697 x represents 'multiply' in mathematics.

[@mike60521x]

@@Humanity101-zp4sq maybe I am old school, but parenthesis, *, x, or a "dot" was always used to signify multiplication we always used an cursive x to represent variable x - so there was never any confusion I have never seen someone use 2 Cs to represent an variable x until this video

[@geirbalderson9697]

@@Humanity101-zp4sq I understand that. I was agreeing with q-tuber.

[@mattpanz609]

Me: I want to go to Harvard to be a history major Harvard: here, take this math test

[@stevetaylor5382]

I want to go to harvard to be a physics major. Harvard: Here, you have to take this class on the history of art.

[@hewitc]

Harvard: Take these wire instructions to your Dad. Tell him to solve $1,000 squared times $5.

[@ConceivedSorrow]

I solved it this way: x³-x² = 12 Extract common factor x²(1-x) = 12 12 can be written like 2²•3 (prime factorization) so: x²(1-x) = 2²•3 And comparte the factors: x² = 2² 1-x = 3 x= -2

[@kingsircheng4540]

👍

[@johnsmith1953x]

That's only one of the answers=FAIL.

[@johannesvalks]

but it is mathematically incorrect. you miss 2 of the three solutions...

[@lashamez]

Solution only works for integers, not real numbers

[@thebig12conference73]

AND YOU FAILED! x^2 - x^3 = x^2 (1 - x) and 12 = 2^2 x 3 but the problem is that we choose x = 2, we don't have 1-2 = 3. No problem, just replace the 2 in -2 because 2^2 = (-2)^2. To recap, x^2 (1 - x) = (-2)^2 (1 - (-2)) , so -2 is a solution. Then, just factor by x - (-2 ) to get x^2 - 3x + 6 and check that there are no other solutions.

[@jbourdette]

The choice of 8 and 4 looks like magic. Be more formal using Gauss theorem about integer roots and soon get -2, the rest is easy, e.g. use Ruffini and Bhaskara.

[@mathis8210]

It looks like magic, because it is. He is just guessing the solution and calling that the "proper method".

[@The_Mega_AnalistSci]

I just do not know why is he doing that and not doing by Ruffini´s method which is x10 times easier and you get the result faster.

[@lefterismagkoutas4430]

this is actually the quicker method if you know what a^3+b^3 is equal to, without needing to use any other method, he just does it very analytically.

[@The_Mega_AnalistSci]

@@lefterismagkoutas4430 Have you even seen Ruffini’s method.

[@celestine5340]

Different approach: a bit trial and error gives x=-2 as a solution. So dividing the whole equation -x^3 + x^2 -12 = 0 by x + 2 gives -x^2 + 3x - 6 = 0. Which is quadratic, and thus solvable -> but has only imaginairy solutions. I think doing it this way is easier than the method used in the movie.

[@ItsVideos]

Interesting. Thanks. Note that the video method also does a bit of "trial and error" when searching for powers of 2 that sum to 12.

[@christianeb8494]

Exactement.

[@BobJones-rs1sd]

To be a bit more rigorous in finding the first root: one should immediately note that a cubic equation will either have three real roots OR 1 real root and a complex conjugate pair. (Complex roots always come in pairs, which means an odd order polynomial always has at least one real root.) Next, note that the Rational Root Theorem restricts any real rational roots to factors of 12 here. (The Rational Root Theorem states that any rational roots of a polynomial equation are factors of the constant term (here 12) divided by the coefficient of the highest power term (here 1).) Any cubic problem like this on an exam will have a rational real root, as otherwise it would likely require using the general cubic formula to solve with nested cube roots and square roots -- and unless you've specifically studied that formula, no one expects you to memorize it. Inspection of the form tells us to get a positive number on the right side requires that X be negative. So, just start plugging in negative factors of 12: i.e., -1, -2, -3, -4, -6, or -12 are the only possibilities. -1 doesn't work. -2 does work. Done. Divide polynomial by x+2 and proceed as you said. Yes, random guess and check could work in this case since the root is a very small integer. But noting the required type of roots and what possible rational roots exist could narrow down possibilities for more complicated equations where the root isn't an integer or is larger. And would be a lot quicker and less error-prone than the method shown in this video.

[@ericr2646]

I worked out before I saw the youtube, on the right hand side of the screen, first of all X would have to be a negative number, so lets try X = -2, -2 squared is 4, -2 cubed is -8 take 4 - - 8 = 4+8 = 12, of course it is good to watch the youtube in case X is not so obvious.

[@billcook4768]

Since when does Harvard have an entrance exam?

[@redskytitan]

If Harvard had an entrance exam based on merit its Asian student population would approach 90%, at least 🤣

[@dasimon123]

It doesn't. I know many recent Harvard undergrads, and they never had to take any special Harvard exam. Plus one can look these things up.

[@nobodynemoq]

come on, it took me a split second to figure out it's a small negative number and another second to ensure it's -2

[@geofwassell]

Simple mental arithmatic gives an answer of minus 2. I doubt that Harvard is this easy. Oh the complex issue: the problem itself ridicules the reason for complex numbers.

[@vegenzohrabian5340]

jesus f christ, don't you have more paper.... great problem, but sloppy work

[@dragonkitsuneGD]

What? This is just a simple cubic equation

[@felipegaeteroman]

X with 2 c's 🫣

[@barneynisbet6267]

-2 seems obvious. Then divide x3+x2-12, by x+2… then show that quadratic has no real roots….then find the complex roots. Or sketch the graph with intercepts and max/min and or points of inflexion….to show only one real solution… Seems like a beginner’s question to solving cubics.

[@christianeb8494]

Tout simplement.

[@DanoshTech]

Bro for Harvard entry solving a cubic equation is very basic and i fell you should be required to find the complex solutions which are (3+-i√15)/2

[@devastationofmankind3495]

So...for everyone thats not understinding the joke...yeah no me neither i quite literally have a grand total of ZERO idea what he's doing after the 4 step...but hey, neither do you...

[@niravelniflheim1858]

Thanks to those explaining that there are 3 answers to find and various methods to get to the complex ones. -2 was always the easy part.

[@brainhuman7609]

The first thing to remember is when there is a power 3, you need 3 answers, that could be enough bring you to a uni. The rest is what method most students could find them if they remember rule 1

[@CandiceJoergan]

With Harvard's new entrance standards, the hardest entrance exam question would be "2 X 6 = ?" Half of the applicants would answer 8.

[@georgestewart3924]

What? You cant take a positive number and subtract a bigger number and get an answer more than zero so x must be negative. Is it -1? Nah. Is it -2? Oh yes. Sorry I guess Harvard's not for me.

[@ScientistPrepper]

Your letters are a dreadful disservice to the english language. You don't know how to write the letters b, x or A. It's a shame.

[@KrystianMichalski]

x=(-2)

[@luciu1001]

Guess the x=-2 Factor the expresion using polynomes rules Solve for cases Way easier

[@BKKGarrett]

What entrance exam??? Harvard doesn't have an "entrance exam". Also, if I were testing a kid for admissions, I accept the clever kid who just looks at it and reasons that it has to be -2.

[@pbworld7858]

For Harvard, I would have expected the student to also find those two complex numbers, and not simply say they're complex. Maybe someone can double check, but I got (3+_sqrt(15)i)/2

[@YainVieyra]

Yeah, because all they need to know are anecdotic calculations 🤦

[@Cotronixco]

Your X is a reverse C followed by a C, and your 1 is a 7? Why?

[@taemagic]

-2 (just solve in my head)

[@q-tuber7034]

I call bullshit on “Harvard entrance exam”

[@JustinTime-fr8fo]

imaginary math is so diverse and non discriminating it makes the word a better place.

[@ТочкиЛагранжа]

Even before I started to think, my intuition said me to check negatives. Then, it is a sum of square and third power. 4+8, so, the answer is -2. This is the solution if the problem is supposed for 12-years old children. For Oxford, you also need the complex ones

[@joseluisf7808]

Even for Oxford, nowadays, I have been told that you should approach problem solving from a non-binary gender perspective as well.

[@tudvalstone]

Writing 12 as a sum of power of 2 just shows you knew the answer. It's easy to eyeball -2 as an answer and make up a "solution". What we need is a way to solve any such equation, not just one where we know the answer from the start.

[@MrKovalius]

Using theorem about the rational roots of a polynomial with integer coefficients, you can guess that -2 is a root of the polynomial, which is obtained by moving everything to the left side. Then, by Bézout's theorem, you can divide the polynomial by the binomial (x+2), and then you get a quadratic trinomial.

[@nicolasbourbaki8896]

you should realize the answer x =-2 directly just by looking at it

[@RaceSmokie]

Totally agree, it is obvious that x can not be 1 or 2 or 3 ,,, it must be in minus ,,, so -1 does not work, -2 ,,, voilà! What a waste of time with all these calculations, and who cares about complex roots, what is the use of it?

[@wolfrogamer6116]

You see if you don't do this type of work you must realize that what your doing is not math but telling the answer or guessing the answer from your own experience

[@RaceSmokie]

@@wolfrogamer6116 what's the point of writing a dissertation on something totally obvious at first glance. Is it that what they waste time on Harvard, to learn how to blablabla on worthless things or they learn how to make elephant from the fly. Where you will use all of these equations? I dont get it.

[@wolfrogamer6116]

@@RaceSmokie haha so you think the study or math is useless or who study physics or maths are just a bunch of nerds Well in that case you are quit wrong because this "useless equation" are used everywhere. At least every where in the digital world. You see we talk to our computers even our mobile phone through these so called useless equation and if math had not existed how you would have gone through space or even figured out how old something is. I don't know about you but I am a computer science student and I have to create equation for my requirements and I use math to calculate almost everything. And I said that work is nessesary, I said it so because through these steps you can prove that you actually did it. You didn't just cheat off someone else. Now I do get your point that if you just want to know it by your self, you don't want to prove anything to anybody but even then you are still performing these steps and by experience you know the answer.

[@RaceSmokie]

@@wolfrogamer6116 actually you are wrong bcz I dont think that math is useless. now, tell me where you have to use whole that process and what is use of it if you just can see the result without any calculation, what is a point to do all of this. Exactly where will be useful to do this equations. What to prove? Obvious things? Pure waste of time.

[@ShifatulIslam-cy3ne]

x^2-x^3=12 the answer is x^2(1-x)=12. x^2=12\1-x . x=√12/1-x =2√3. Thanks 😊😊😊

[@ShifatulIslam-cy3ne]

❤

[@virag1132]

pro tip: harvard doesn't have an entrance exam lol

[@gravidar]

Sorry, the "logic" to get to 8 + 4 is just guessing, once you start introducing bigger numbers and perhaps even non-integers this breaks down entirely and doesn't solve the problem at all.

[@christianeb8494]

-2 est racine évidente, il n'y a plus qu'à faire une division polynomiale par (x+2) pour ramener cette situation à un polynôme du 2nd degré? Concours d'entrée pour Harvard? Pas besoin de monter une usine à gaz.

[@DoubleplusUngoodthinkful]

This is the first time I have ever seen the letter "X" drawn as back-to-back Cs.

[@robertvavra414]

Gives new meaning to 'extasy'. (sorry)

[@ChristianRThomas]

Really? Are you still in your pram?

[@DoubleplusUngoodthinkful]

@@ChristianRThomas "pram"? Are you still in the 1800s?

[@ChristianRThomas]

​@@DoubleplusUngoodthinkful Don't be silly! I'd be calling it a perambulator if this were the 1800s.

[@MartelloClaudio]

Smart solution method. I used anothet method: starting from X^3-X^2+12=0, I used Ruffini's solution method by just seeing that X=-2 is one of the solution of this equation. Then just follow Ruffini rule and get to the same solution in a while

[@georgegreen-b3i]

lost me when he started talking

[@MandyFlame]

Factor directly as (x+2)(x^2-3x+6)=0 (By inspection x=-2 is a solution, then just work out the other bracket)! Then solve the second bracket using the quadratic formula to find the complex roots.

[@TonalWorks]

Yeah, I did exactly the same just by inspection/ reasoning: (x+2)(x^2 + ? + 6) = x^3 - x^2 + 12. Btw: Why is he only solving for real x's? It's not obvious from how the equation is presented in this video. I hope the Harward problem was more clear regarding the set of solutions.

[@santiagoferrari1973]

Much better than the long way in the video

[@TonyRedunzo]

who gives a $hit about harvard

[@wilson2455]

certainly took the extra long way for something I did (in my head) in about 10 seconds !!

[@RavenMobile]

What is all this nonsense? # N=1; (N*N)-(N*N*N) = 0 # N=2; (N*N)-(N*N*N) = -4 Okay, that is heading away from 12, need to go the other direction. # N=-1; (N*N)-(N*N*N) = 2 # N=-2; (N*N)-(N*N*N) = 12 Done.

[@AlexEckelberry]

Just do some guesses. Guess by pretending x = 2, then x = 1, then -2, etc. to find it. It doesn't have to be so complicated. And you can also just go to Harvard extension online these days - there's a 4 year degree online that if you pass the first class, you're in. It's hard but it will be a Harvard degree.

[@BruceLee-io9by]

It's easier to break down the polynomial using Ruffini's method.

[@alexlucky3338]

Exactly my thoughts) but it's good to have an alternative method in mind as many people are "allergic" to polynomial division 😅

[@EddyGilley]

I liked Raffini in #LionKing. When he held up Simba on Pride Rock before all the Pride Landers to see, it gave me chills. Circle of Life. #RaffinisRule 😉 Semper Fi

[@italixgaming915]

WOOOOOOOOOOWWWWW you COMPLETELY overcomplicated this poor little thing. Here is how to destroy it... First of all, we're looking for integer solutions. Instead of regrouping on the same side, let's just factorise both sides: x²-x^3=x²(1-x) and 12=2²*3. The similar formulas suggest us to test 2 and -2 and indeed -2 is a solution. You can also see that -2 is even the only real solution: x²(1-x)=12 implies that 1-x>0 or x x²(1-x) is continuous and strictly decreasing, which means that it can reach a given value only one time. Saying this is optional. Now you write x²-x^3-12=0 and since you know that -2 is solution you can factorise by x+2. You obtain: (x+2)(x²-3x+6)=0 And you can solve the quadratic equation if you need the complex solutions.

[@qzwxecrv0192837465]

wait, many people failed this simple math problem? i did it in 10 seconds in my head: (-2)^2-(-2^3)=12. Given you have to subtract the second number, the root number has to be negative in order to ADD it to the first number. so simply, using 1 for x, we get 1-1=12 WRONG, with two we get 4-8=12 WRONG but change the sign to + would make it work, thus -2. no need for long formulas, quadratic equation, etc. for such a simple math problem.

[@satautenyo]

then the solution depends on FIGURING 12=8+4... in this case is also valid FIGURING that x=-2 is the first solution (trying integers by hand) and dividing the cubic equation by (x+2) which yields x^2+3x+6=0 and then the roots are 3/2 +- sqrt(15) i /2 as said by other mates... I don't think mine nor author's are valid and FORMAL solutions anyway...

[@jbjohnson4728]

Why can't you do x^2 minus x^3 equals x^-1 = 12. In basic alegbra (my level), I was taught that x^-1 = 1/x (1 over x). Set that equal to 12 and solve for x and you get 1/12. If I plug in 1/12 into the original equation I obviously don't get the right answer, but it seems like my method should be right based on the basic algebra I was taught.

[@IITJEEAspirant2025-fj6hj]

x²-x³=12 =>x²(1-x)=12 By trail and error , Factors of 12 are 3×2×2 Now to get , the answer is a positive number But the factors we get x² is positive but there is a problem with (1-x) if 1>x then we also have to consider x in the range of negative number and we should also connect with the negative Factors Hence,we consider the Factors to be -3,-2,-2 By trail and error if we put x=-2 We get 12!

[@jofel131]

Correct but very long. Surely the solution must be negative, because x^n is strictly increasing as a function of the positive integer n > 0, if x > 0. Morover the solution must be small, because x^2 - x^3 increases very fast as x < 0 decreases. So, before calculation, just try with -1 and -2. Alternatively you can write x^2 - x^3 = 12 as x^2(1-x) = 4 * 3 and realise that 4 = (-2)^2 and 3 = 1-(-2), using intuition. Since the function x^2 - x^3 strictly increases as x < 0 decreases, it can be equal to 12 at just one real x, so the other two solutions must be not real.

[@moho_sama]

I don't know the american standard about mathematics but even a simple student from any highschool in italy can do this. Just find something make zero so x=-2 and just go on with Ruffini's technique. And is the same as the video x1=-2 x2,3= complex. And at university they teach me to converting the negative root to i(sqrt) of 15 so x2,3 will be: 3+i(sqrt)15/2 and 3-i(sqrt)15/2 Very impresses cause i think is simple but i repeater i'm in italy and i don't know about the mathematical standards in us.

[@Dismythed]

Why do you have to prove that -2+2=0 ad nauseum? Once you have guessed (and it is a guess), that x³ is 8 and x² is 4, the minus turns x into a minus. The only proof you need after that is (x³-2²)+(x²+2³)=0 (or -12+12=0). All the other math you showed is a bunch of 0+0=0 or 0x0=0. It meant nothing.

[@FreeSpeech181]

Why the heck would anyone need to know this if he or she is NOT majoring in math?

[@gaynzz6841]

They don't. Rich parents pay millions to the school, their kids don't need to pass any exams.