Oxford Entrance Test Question Solved in Seconds

[@alexanderklychkov6716]

If you see "trigonomonster" arguments, powers, coeffcients etc then you know this kinda of task where you should use absolutely legal logic cheat

[@spencergee6948]

That's a lot of 'several seconds'!

[@sou7851]

If you do it in your head it’s only gonna take seconds tho :)

[@lucasnite7600]

For sure! After all, elaborating on the steps was the whole point of the video : )

[@v1cky889]

Yeah man...

[@fink7968]

How helpful would it have been if he just solved the question in his head and wrote the answer? This is a video explaining how to solve it, if you learn math, you can solve it in seconds all by yourself instead of whining on the internet.

[@Music-hz3os]

@@fink7968 dude it was a joke chill

[@subhrayanbarman1654]

By observation, 4≤LHS≤16 and 2≤RHS≤4 . So, LHS= RHS when both sides are equal to 4 which occurs at cosx= -1. X=π+2nπ Edit- Almost same solution

[@霍金本人]

You wrong

[@Piemanray314]

@@霍金本人 No he's right wym

[@霍金本人]

@@Piemanray314 you wrong. They are exactly the same solution not almost.

[@Piemanray314]

@@霍金本人 Thank you for the irrelevant observation. His solution is still right.

[@alaechoulli6111]

Yesss!!

[@DrCong]

This can be solved via Pythagoras's Theorem. Set c = 2, b = 3 + cos x, a = sqrt(2)*sin^4(x). Then the given equation is b^2 = c^2 - a^2. Hypotenuse of right-angled triangle is 2, the other sides are sqrt(2)*sin^4(x) (which is always non-negative) and 3+cos(x) which is always greater than or equal to 2. So the only possible solution is sqrt(2)*sin^4(x) =0 and 3+cos(x) = 2, i.e. when sin(x) and cos(x) = -1, i.e. when x = (2k+1)*pi, for any integer k.

[@Jim-be8sj]

Clever. I like that approach.

[@fahrenheit2101]

Ah, I've never considered looking at the ranges of LHS and RHS - thanks for the tip.

[@arpangoswami5760]

I found a geometric solution😅😅. let's consider the ellipse: x²/4 + y²/2=1. clearly ((3+cosx),sin⁴x)lie on this ellipse. Ends of the major axis of the ellipse are (2,0) and (-2,0). for the point to lie on the ellipse: -2=

[@arvindiyer1649]

Big bren _ /\ _

[@xhajssoa9565]

Arnab goswami

[@arpangoswami5760]

@@xhajssoa9565 reporting straight from Republic India 💣💣

[@pranav3851]

@@xhajssoa9565 THAT IS A CURSED NAME

[@joshavery]

"clearly"

[@varunraj8606]

2^2 - (3+cosx)^2 = 2.sin^8x (-1- cosx)(5+cosx) = 2sin^8x (-1)(1+cosx)(5+cosx)=2sin^8x now lhs gives us a non positive value and rhs gives non negative value implies lhs=rhs=0 is the possible solution if exists 1+cosx=0 and sinx=0 therefore x= odd multiple of pi

[@abyss713]

2nd step?

[@varunraj8606]

@@abyss713 a^2-b^2=(a-b)(a+b)

[@abyss713]

@@varunraj8606 🤦‍♂️

[@simongross3122]

Really interesting approach

[@SQRTime]

Hi Simon. If you are interested in math competitions, please consider kzbin.info/www/bejne/npjKimCXd7x6e7M and other videos in the Olympiad playlist. Hope you enjoy.

[@eduardoteixeira869]

I believe to solve this problem is easier if you bring to the left side of equation the term 2(sinx)ˆ8, then you get (3+cosx)ˆ2+2(sinx)ˆ8=4. Now if you think, you have to positive numbers that added gives you 4, then it is not difficult to conclude that the only possible solution is when cosx is -1. Thank you

[@NEPtune-fy1ug]

thats a terrible way to solve this

[@angelmendez-rivera351]

@@NEPtune-fy1ug I agree.

[@jyle4420]

@@NEPtune-fy1ug What do you find terrible about this solution? I believe it is a wonderfully unique approach to this otherwise intimidating question

[@NEPtune-fy1ug]

@@jyle4420 there's such a big leap between "positive numbers that add up to 4" and "not difficult to conclude that the only conclude that the only possible solution is when cosx is -1". if the solution is just by observation, its trash.

[@Lucaazade]

Rearranging the equation doesn’t change it in any way so you’re doing exactly the same thing, but sure, I think that makes it even nicer too. The video is only minutes long because it’s an explanatory video, not real footage of his brain. → 4 is the only way LHS = RHS because I can imagine the values of squares and subtractions → cosx = -1 and sinx = 0 → x = pi is immediate.

[@federicopanichi9874]

Incredibly smart approach. Out of curiosity, what tools do you use to draw on screen? Great vids !👍🏼👍🏼👍🏼 👍🏼

[@saiyamsoni2664]

Finger

[@c2h5oh32]

@@saiyamsoni2664 Fingers definitely.

[@giovannifrrri5495]

iPad pencil or pen

[@DrMaxPlank]

it is not smart just when you deal in things like trigonometry for longer period then you will know various of solutions... for example I use xournal++

[@youtuberbooster6422]

Very interesting ✨!! More more plz gentleman 🙏

[@mzterzi]

Can you please explain your reason for the domain of sin^8(x), after the first line on the right side. Thanks

[@yavuz1779]

It it raised to an even number so it cannot be negative because it is a real number. So that's why it is between 0 and 1

[@mzterzi]

@@yavuz1779 I thought the lower bound would also be 1 because (-1) ^8=1 but that wouldn't make sense because the upper bound is 1. Why zero?

[@fejfo6559]

@@mzterzi sin(0) = 0 The lowerbound of x² isn't reached at the endpoints of [-1,1] but at 0

[@mzterzi]

@@gytoser801 teshekkur

[@mzterzi]

@@fejfo6559 thanks

[@refrezhmz8166]

I really hated highschool math. Idk why, but when i watched this video I think the problem is not the math. It’s the teaching system.

[@whyamisad5740]

Same here. I'm writing my A-levels currently, and whilst studying for the maths exam, I've come tonrealize that maths actually is quite fun to do. Even though certain questions, such as the one in this very video, would still be impossible (right now) for me to solve.

[@refrezhmz8166]

@@whyamisad5740 True!

[@abdullahh283]

I believe math is a skill everyone should learn, it improves one's logic and analysis greatly. And I agree school systems butcher it to be a unlikable, but hopefully this issue resolves itself in the age of internet.

[@paulu_]

This is high school math, though.

[@refrezhmz8166]

@@paulu_ yeah im telling the reason why i hated highschool math.

[@SajoGotoru]

Never thought it like this that we can solve trigonometric equations by equating their probable ranges. Is this AP maths ? This type of solving was not taught in high school trigonometry.

[@jacekstankiewicz1594]

This is a waste of time math, solving equations is a useless skill

[@eyeris4050]

@@jacekstankiewicz1594 funny because your phone wouldn't be working unless a couple equations were solved here and there

[@EMC273]

@@eyeris4050 right

[@amritrajsingh7434]

This is actually a higher level of solving trigno equations which is generally not taught in schools

[@ronaldjensen2948]

@@jacekstankiewicz1594 I've made quite a few dollars solving equations...

[@youspin8826]

You could do this grapically by sketching the curves Y=(3+cos x)^2 and Y=4-2sin^8x with the x axis marked in increments of pi - observe the points of intersection of these two oscillating lines. The first line oscillates between 4 & 16, and the second line oscillates between 2 & 4. Therefore the only way they can intersect is if the first function is minimised and the second maximised for the same value of x.

[@waltermalone]

WOW I respect u I didn't catch the range first! Good video!

[@mathisnotforthefaintofheart]

I did trial and error to find x=pi. Took me about 10 seconds.That of course is not a guarantee that it is the only solution. I don't recognize the significance of such a question to get admitted in a prestigious institution like Oxford.

[@isaacmalik3714]

i actually expanded the whole thing and simplified, then noticed the cosx part was a quadratic equation (sub cos to be x and solve for x) which gave -5 and -1. Reject -5 like you said in the video to get -1. I didn't know how to do the rest but yeah

[@abhikalpshekhar]

it is a commin trick in trigo to check range in cases where nothing in the expression factorizes or cancels etc

[@MrLidless]

Oxford entrance exam for mathematics? That’s like going to Cambridge to study ancient Greek. It’s just not done.

[@anawilliams1332]

Oxford has alot of good mathmiticians

[@angelmendez-rivera351]

You really don't know Oxford, then.

[@skrill500]

Andrew Wiles, the legend who proved Fermat's Last Theorem, is a professor at Oxford. Surely he would pick an "inferior" institute like Oxford over Cambridge...

[@MrLidless]

@@skrill500 up to the age of 18 he was schooled in Cambridge and his father was chaplain at one of Cambridge’s affiliated colleges. So he was well-prepped to study maths at Oxford having already learned the course. We prefer not to talk about his losing a legendary drinking game that involved a pig and a dwarf in a tutu that had him banned from the city for life. A pity. Imagine the heights he could have risen to had he refused the challenge and been allowed to study at Cambridge.

[@spaghettiking653]

@@MrLidless Can you share where you get that story, that drinking game one? I tried looking up "andrew wiles drinking game", "pig", "tutu" etc., but stumbled upon nothing. (Also youtube likes to shadowban comments with links, so just a title or something will do)

[@Nathan-yu7cu]

I think the guess and check method works the best lmao. just go through the unit circle and call it a day.

[@amlan342]

Solved in seconds though 🙃. Even millenium has many trillions of seconds.

[@willbishop1355]

But what if x is a complex number? (Granted that's not what the test was asking, if it specified 0

[@armagor4828]

What is cos(x) for a complex number?

[@willbishop1355]

@@armagor4828 en.wikipedia.org/wiki/Euler%27s_formula#Relationship_to_trigonometry

[@armagor4828]

@@willbishop1355 What i wanted to say is that cos isnt defined for complex numbers, so your question is nonsense.

[@willbishop1355]

@@armagor4828 You asked how cosine is defined for complex numbers, so I gave you a Wikipedia article with the definition. You are completely wrong to say it's not defined.

[@armagor4828]

Ok i didn't know, my bad

[@nightking8490]

First thing I did was to check for 2n pi and (2n+1) pi as guess, and guess what (2n+1) pi is satisfying it all.

[@JeffMTX]

always check the limiting cases first!

[@Fac31ess]

im not in oxford, im not even in any of the first world countries. Im actually in one of the worst universities ever but this is one of the easiest questions ive ever seen

[@lukaide6359]

How so

[@salvadorfindley3555]

it makes sense but never in a million years would i have solved it myself 😹

[@shs2247]

Literally just after seeing the question i put cos x=-1 and got the ans in "seconds"

[@myke5696]

I dont believe this problem was actually used to see if a high school graduate gets into oxford. Setting both sides equal to 4 is too arbitrary.

[@Lucaazade]

Is 4+n = 4 also too hard because 4 is the value for which they are equal?

[@Aqua17292]

How do you get Latexed equation in the slide? Latex option is not available on slides

[@zadsar3406]

You can always just screenshot the equation and paste it into the slide.

[@raphaelmarquesfranco1060]

please where I find Oxford hard ones?

[@mohammadhanouf2116]

In 1:26 How the one become zero if he added to it -2 Iam not understanding this part

[@peki348]

You multiply by -2 so the sign changes 0*(-2)=0, 1*(-2)=-2

[@peki348]

When you multiply by minus you also switch the sides of the equation

[@mohammadhanouf2116]

@@peki348 Thanks for your help

[@Loots1]

Seconds?? What do you define as a second?

[@edwinborrison703]

Lazy solution, when running out of option 😅:- 1. Range of sin X is [-1,1] , now (sin X)^8 would be a much smaller value hence ignoring it for the time being. 2. Now, ( 3 + cos X) ^2 = 4. Indicating, ( 3- 1)^2 is also 4. 3. After comparing, cos X= -1, hence x= π

[@AnmolKumar-dh3lh]

fuck man did this in junior high school

[@user-vo2et6ho4h]

ROFL .....When i see the thumbnail i laughed and start rolling While I start regretting that why i am not born in UK Btw being Asian and gonna give jee entrance exam...i can say non-asians are luckiest people in this world

[@lucasmartiniano6915]

"Asia is better in maths we knew how to solve this before even being born blablabla" what's the point of all those comments seriously...

[@EnergiaII]

My answer was cosx=7 and cosx=-1 since it gave me a quadratic equation, but since cosine can't be bigger than 1 the answer is cosx=-1 so x=180°

[@parsakhavarinejad]

These kinds of questions are considered "easy or normal" at high school in my country.

[@tylosenpai6920]

My trick was to get the key values for cos and sines, i got a solution... And it was (2n+1)Pi

[@Alex_AFC]

I couldn't calculate that if my life depended on it

[@CliounPlayz]

lol same

[@Greg-oy1vf]

I'm not gonna lie to you but this is rather easy like I could have done this under 1min before watching this video.

[@shubhamjha6418]

which inequality method is this? can anyone tell me the method name?

[@Lucaazade]

a ≤ b and a ≥ b implies a = b is called the antisymmetric property of an ordering relation but you can think of it as “less is the opposite of more and there’s a third option which is equality”.

[@qupie358]

SEA student here. Could confirm this is only 9th-10th grade math problem

[@johansyah9579]

I think here is not that complex

[@IconicFootball]

I solved this in 10 seconds because I got impatient and just guessed and checked pi for x and got lucky that it was correct

[@koalabear8953]

We get this solution by , using try and error method , Always use 3 values -1,0,1 and luckily we get what we want on first try

[@raige3534]

Jee aspirants will laugh if this comes in JEE adv

[@user-vo2et6ho4h]

Well it comes in out jee exam in alternative universe

[@pencilbox2214]

“cause x”

[@loading...2876]

How much time would be allocated for this question?

[@Lucaazade]

This is a single part of a question so it is probably worth about 3 points out of 100 on a 2 and a half hour paper. If you plan to spend your time proportionally then you should plan to spend about 4 minutes.

[@user-dw1zb3fh5n]

I don’t have the slightest idea of what’s happening here. All I know is my calculator got the answer wrong.

[@ig1948]

Step 1) understand wtf you’re even looking at

[@lily_littleangel]

First try cos(x) = 0, which gives LHS = 9. This is obviously way too high so LHS is lower. Trying cos(x) = -1 gives 2² on the left and 4 - 0 on the right which is a solution. Thus x = pi is a solution.

[@SoloPro]

too eay knew a more algebraic way wouldve been elegent

[@cod-gamerz7225]

How many jee aspirants here found this easy af

[@leezudinho]

amazing problem and solution.

[@FandangoJepZ]

Is this seriously for college entrance?

[@ainley487]

Me who was gonna prove the equation instead of solving it 🤡🤡🤡

[@sashindrashrestha6300]

The inequality is supposed to change when negative is introduced on RHS. I think something wrong here

[@MrChatmoon]

Excellent

[@GaetanoCoiro]

Davvero ben fatto. ⚡⚡⚡

[@raven_5180]

My brain is not giving a single crap about all this yet still watching it. Internal pain

[@sirius9436]

I actually was able to solve it just by looking at it under 30 seconds

[@luthandonomzaza1607]

How?

[@bigbadbith8422]

Wonderful

[@MathPhysicsFunwithGus]

Great video!

[@jstone1211]

you lost me on the -2

[@jstone1211]

@Rohit Bobli you are a genius, that is obviuos.. I have since understood HOW the limits were obtained...

[@nikolacvetkovic4549]

He just multiplied both sides with -2. The reason he did it was to get to the 4 (in the next step) to be able to draw the needed conclusion. Note: Effect of negative numbers on inequalities --- Anytime you multiply or divide both sides of the inequality, you must “flip” or change the direction of the inequality sign.

[@jstone1211]

@@nikolacvetkovic4549It has been a long time since I worked with basic functions like equalities etc....at 65 I have to relearn a few basics...but it is fun.

[@tabarnaklovessosa]

i solved it just looking at the thumbnail.. it just came to me lol. it was first thinking even multiples of pi so cos x =1 and sin x = 0 but then i noticed the square so it has to be 2² in Lhs and 4 in RHS which is only in odd multiples of pi since cos x = -1, sin x= 0

[@diegoalgo1296]

So cool!

[@AJ-et3vf]

Awesome

[@VIKASVERMA-nk8uw]

Great work

[@kanabalize]

Year?

[@letsthinkcritically]

2008

[@jewel8482]

My method was just observing (3-1)^2=4 So cosx=-1 and 2sin^8x =0 So (2n+1)pi is soln

[@Lucaazade]

Yes that is the method this video explains.

[@VIKASVERMA-nk8uw]

Iove from India 🇮🇳

[@SQRTime]

Hi Vikas. If you are interested in math competitions, please consider kzbin.info/www/bejne/npjKimCXd7x6e7M and other videos in the Olympiad playlist. Hope you enjoy it.

[@SaidVSMath]

I solved it!!! Woo!!!!

[@daltonomondi2096]

Incredible

[@sberacatalin2250]

👀🙄👍👏🙏🇷🇴👌🙌 Next?!

[@agrajyadav2951]

Really smart

[@U9191-e6s]

very nice solution

[@josemvazquez2259]

I made it more difficult, changing sin²x for 1-cos²x you get a equation with cos(x) ,changing cos(x) for "t" , you get a polynomial of grade 8. With Ruffini the solution is t=-1 or cos(x)=-1

[@yearseventeacher]

Great.

[@Magistrixification]

Neat.

[@thibs2837]

I watched and listened, I couldn't do it rn anyway

[@SQRTime]

Hi Thib. If you are interested in math competitions, please consider kzbin.info/www/bejne/npjKimCXd7x6e7M and other videos in the Olympiad playlist. Hope you enjoy it.

[@MrGameAndToy]

The “solve in seconds” way is just to check common values for x and see if anything works. 0, pi, -pi, etc. As it turns out, x = pi is a solution. From here, you can just extrapolate that into a general solution by taking pi (the solution we found) + some multiple of 2pi, or in other words x = 2*n*pi + pi where n is an integer, however the question doesn’t ask for you to do this. This isn’t mathematically rigorous, and doesn’t help in all questions like this, but for this particular special case it gives the right answer.

[@Lucaazade]

This video is an *explanation* of the “solve in seconds way” where you see that (3+cosx)² ≥ 4 and 4-y ≤ 4 therefore x=pi. Theoretically, finding a solution isn’t the same as solving it, because if there was more than 1 solution then you wouldn’t have found it. But this question relies on it being an extreme value of cos x so if you try both 0 and pi then you gottem.

[@rutger_greve2926]

pi + 2(pi)n

[@rutger_greve2926]

Extremely easy

[@chrismanson3211]

clever

[@miracletalks8025]

IITans - We can solve this actually in second !

[@yoav613]

It is easyyyyyyyyyyy.solve it over the complex,to make it more interesting.

[@tianqilong8366]

True hahaha, but this method is kinda interesting as well, rather than hard solve it

[@aviratnakumar5847]

You can apply the sun of square of the sinx and cosx as 1. But that will give an octic equation whic is very long. And from that you will get cosx as -1 as on of the solution and of the 7 solutions can be either all irrational or 1 real solution that too irrational and rest of them complex and so on. Please try them at your own risk

[@zayn7601]

@@aviratnakumar5847 the octic can be solved relatively quickly using synthetic division and just testing factors of 1 and -1

[@xtehmoonlight7400]

you might as well say 200 seconds

[@cvmaths9838]

Poor explanation, just move the sin, that is a square, on the other side ! without any calculus, it s obvious (as sin and cos cant cancel at the same time)

[@angelmendez-rivera351]

There is no need for them to cancel. You are saying nonsense.

[@cvmaths9838]

@@angelmendez-rivera351 Now i see who good and who is not

[@Triggered_Carefree]

I dont understand

[@tanishqchhabra3084]

I hv another solution (am a tenthie idk why imma watching this) So, LHS×0=0 RHS×0=0 Here LHS=RHS HENCE PROVED ND OFCOURSE THIS WAS A JOKE

[@froku3531]

Why am I here I’m in set 3

[@finleyjohnson4193]

Thats alot of seconds

[@kamranjeetsingh8610]

I solved it in a minute or so # jee advanced aspirant

[@gradientattack]

easy 🤔

[@liangeloball8322]

Damn so like if yk yk

[@MR.LOCAL-X2]

Why I click this?

[@peacefulphysicist8535]

Trivial

[@davidesessa5008]

.

[@phoenix-quennazula3919]

I can solve this with mi Calculator in 16 sekonds

[@95MarioKaci95]

Its a bad exercise, u do a lot of work hopping that boundaries match, what if they dont u wasted time on an intuition

[@amanbhaskar3913]

Appreciate the efforts, but you've made the solution unnecessarily complicated

[@titfortat4405]

What is an easier solution?

[@malarvizhiveliah6846]

@@titfortat4405 Just compare the range of LHS and RHS , u get they only solve at when they are 4

[@titfortat4405]

@@malarvizhiveliah6846 That's what the video did to derive the solution. I was asking if there was an easier way than comparing the LHS and the RHS like done in the video.