I'm going to introduce another term, y = sqrt(x + 13) + sqrt(x - 3). Then, we can multiply the two equations together: 2y = (sqrt(x + 13) - sqrt(x - 3)) (sqrt(x + 13) + sqrt(x - 3)). But that's just the difference of squares formula, which gives us 2y = (x + 13) - (x - 3) = 16, so y = 8, so sqrt(x + 13) + sqrt(x - 3) = 8 Then, we can add sqrt(x + 13) + sqrt(x - 3) = 8 and sqrt(x + 13) - sqrt(x - 3) = 2. So 2 sqrt(x + 13) = 10, sqrt(x + 13) = 5, and x + 13 = 25, so x = 12. In essence, conjugates are amazing and you should look to abuse them when you can.

That's the correct way to do by taking square both side. However in this particular question since value is 2. We can even try hit and trial with difference between number as 2. The first number has x+13 so that number can be minimum 4 if x is 3. Try keeping x=3 we will get 4 -0 =4 so x=3 not correct. Next x+13 will be 5. For that x=12 and yes it satisfies 5-3=12. Again what I did worked here because the number was small. However the best and foolproof method is square both side🙂

Honestly I didn't understand anything, but i watched the full thing, great explanation 🔥, keep it up !

Interesting Btw at 2:25 I think you were mentioning the notable identities This one in particular: (a + b)² = a² + 2ab + b²

(x^2-8x)+(y^2-4y)=3 add (8/2)^2 or 16 to x to make it a perfect square and (4/2)^2 or 4 to the y to make it a perfect square (x-4)^2+(y-2)^2=3+16+4 (x-4)^2+(y-2)^2=sqrt(23)^2 form of the center being (h,k) and radius is r for (x-h)^2+(y-k)^2=r^2 so the center is (4,2) and the radius is sqrt(23) good algebra 2 problem!

Algebra Baldor is widely used in Latin America, I have a very old edition, with beautiful illustrations. If you can take a look at "Matemáticas simplificadas" by CONAMAT.

Great explanation 👍

The extra y variable really confused me

thank you!

top notch way to go

Sublime

noice

Another approach to the problem is to divide the 144 miles by 4 hours to get a combined speed of 36 mph. If x is the speed of the slower train, then x+(x+6)=36, yielding the same answer. Final observation: if the speeds are only 15 and 21 mph, the trains must be hauling freight.

thankyou!

First 🥇

Can you explain removing the negative i in the beginning

Thank you for answering my questions! I apologize for not mentioning my current maths level in my previous comment. I am currently enrolled in an gifted students program in my school, and am proficient in maths upto a 9th grader. The school provides me with free PDF for these higher studies books. However, they only provide upto 3 books per year. I will surely follow your advice on openstax and other resources. Thank you very much!!

Hi, I am a 7th grader. All the maths textbooks such as by Blitzer, Spivak, and Stewart are sold at an atrocious price in my country. Their PDF(s), however, are available. Do you have any tips for me? I have no intentions of joining maths as an researcher/professor, insead I am focusing more on my physics. I would like to start learning physics as soon as I can. Should I instead go with Khan Academy or the series of textbooks followed in my country (NCERT's is the name of the series)?

Hidden quadratic so you could use quadratic formula and remove extraneous solutions

I put a comment so you can get more views 👍

Doing a U sust. U = sqrt x. We have U^2 -U -6 = 0. (U-3)(U+2)=0. Then Sqrtx = 3 implies x = 9. but sqrtx = -2 don't exist!.

Thanks. This helps with application problems. Not my favorite 😅

Very nice

Learned Something New . Keep The Hard Work , Maths As A Subject Is So Important .

Easy make it harder

Keep doing

Amazing how simple ot seems yet so complex.

A pie pi wide is pi square around.

That is an annoying problem. I tried to solve it myself and got it wrong an uncountable amount of times 😂

i like blank sketchbooks. they combine the foldability of spiral notebooks with the freedom of blank printer paper

Thanks so much for making a whole video about my question! I really appreciate it! Btw I am a Slipknot fan as well.

I am in 6th grade and have started working through Intermediate Algebra by Tussy and Gustafson because I want to learn more about mathematics. I also got College Algebra by Blitzer. Do you have any tips for me?

A- in summer math , soef studied with prof leonard 2x and while being sick 5weeks 3 days

Thanks bro 👍

The video would be better with a different example. Let y = (-2x + 3) / 2, and it's obvious that 6 <= y <= 1 has no solutions with needing any algebraic manipulation whatsoever. If a student on a test said there were no solutions simply on the basis of inspection, well, I'd have to agree.

This guy is the Joey Chestnut of math. He just gobbles up math problems.

ps I don't smell them

My marh books library is groeing from watching his casts. EBay has most of them I average $8.00 per book.

Not knocking CCs, but a math major is going to have a harder time in his junior and senior year at a regular university. The strong math majors are arriving for their freshman year at 4-year schools with AP calculus BC already under their belt.

this looks so easy! why do people complain about double and triple integrals? do they get harder and are there special techniques to solve those sorts of situations?

A composition notebook would be perfect if you could fold it in half like a spiral... I have a fire tablet but its awful for math because there's no stylus like the apple pen. Does the ipad stop your palm from messing with the screen if you use the pen?

Every latino has bad memories with that book haha

Hello Mr kieju I'm a math teacher and I want some useful books and advices to motivate and help my students. Please if you can.

A difference between universities and community colleges. Opportunity. At a university you have the option to take an introductory proof course at an earlier stage. You can easily fit an intro to proof textbook within your textbook stack. And, you get the chance to interact with faculty in your department, you’ll be able to build relationships with those professors so later you can get letters of recommendation and potentially a research position.

Although Holt and Glencoe maths books, mainly for secondary school, but a lot of information can get from there….

The _Mathematical ideas_ book does look nice.

It sucks that we can all self study this but never get any credit. And i dont just mean college credit. I mean people dont recognize merit through demonstration. I have taught myself from algebra 2 to calc 1. It took a lot of effort. There were time i questiined my own abilites and i wanted to give up. And i still feel that way. Because the average person hiring for a company doesnt acknowledge your efforts or willingness to improve and master a set of skills. The last job interview i had was at a bank. They asked me if i had any accounting certifications or college background. I said no and then began to do a summation of natural numbers in sigma notation, and i had planned on showing how to derive the interest formula. But i was interrupted before i could finish as if i were some crazy person saying something irrelevant and was told they were looking for someone with college/state merit. These people dont even know what i can do with functions and matricies and they wont even let me demonstrate. Too poor to go to college. And cant get a better job without it. We are not a western society that is based on logic and merit. And that makes me very sad.

This is such a great algorithm. I don't know why it isn't taught more often.

Community college excuse for a "math degree" is a joke. Look up some concepts in a uni math degree and youll see what im talking about.

Just finished a 6 week DiffEq class. Three weeks in I already felt burnt out. In 5 days I start another summer class (Math proofs). I am scared......