Harvard-MIT Math Tournament with Interesting Radical Equation

[@MrGLA-zs8xt]

Your channel is a true math youtube channel that is not compared to those channels that repeat same types of the questions with different titles over and over again.

[@drpkmath12345]

I really appreciate the support my friend! 👍👍👍

[@ronbannon]

Black Pen Red Pen did this problem years ago. This reminds me of a Polya quote, "Even fairly good students when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important and instructive phase of the work. ... A good teacher should understand and impress his students that no problem whatever is completely exhausted." In that line, I often redo problems with my own bent and encourage all students to solve the problem their way. Thanks so much for sharing.

[@Min-cv7nt]

As long as i remember, dr pk did this problem before bprp. He posted this years ago first

[@drpkmath12345]

Thanks a lot my friend for your comment👍👍👍

[@domedebali632]

What a fantastic video professor

[@drpkmath12345]

Glad you think so!👍👍👍

[@iqtrainer]

I remember this problem from hmmt professor, very nice video btw🎉

[@drpkmath12345]

Glad to hear it's helpful my friend! 👍👍👍

[@christiannavarro3556]

Sir, why does it need to be less than 20²?

[@viziattila5162]

Because if you take any number for n which is bigger than 0, than the equation 200+2*squareroot(10000-n) would be smaller than 20^2. Otherwise for the function f(n) =200+2*squareroot(10000-n) its maximum is reached when n=0 and the maximum value of the function is 400 (if we are talking about positive integers)

[@drpkmath12345]

Well-indicated my friend👍👍👍

[@mathnerd5647]

You are the legend professor

[@drpkmath12345]

Thanks my friend👍👍👍

[@Min-cv7nt]

Another great video professor

[@drpkmath12345]

Thanks again!👍👍👍

[@ronbannon]

Bounding the expression between 20 and 14 and noting that it must be even, results in two choices, 16 and 18. Both 16 and 18 should be checked. If n=16, then we get 9216, and if n=18, we get 6156.

[@nicolascamargo8339]

If 200+√(10000-n)=16² or 200+√(10000-n)=18² luego por ser 200+√(10000-n) una función decreciente a mayor valor de salida menor valor de entrada por eso se da cuando 200+√(10000-n)=18² no cuando 200+√(10000-n)=16² como es verificable.

[@drpkmath12345]

Thats nice work! Thanks for sharing👍👍👍

[@elix3085]

why cant n be 121

[@domedebali632]

read the question at least once carefully

[@davidseed2939]

The answer is 18x18x19 not sure of significance. i was expecting a perfect square

[@domedebali632]

???

[@POLMAZURKA]

stand to the side...............

[@mathnerd5647]

He usually does

[@ZDTF]

100-n? And N=1? Because 99 is an integer? And 100-n cuz Cuz A^2-B^2=(a+b)(a-b) and I thought it can be used like √100+√n Wait a second ITS A ROOT IN A ROOT? NAHHHHHH THIS IS CHEATING BANNED

[@domedebali632]

What are you talking about? Are you making something up so badly that sounds totally ridiculous

[@ZDTF]

@domedebali632 Bro I swear this sounded logical in my head until I noticed the roots

[@drpkmath12345]

Not really sure what you are talking. Have you watched the video? Not your work but video

[@ZDTF]

@@drpkmath12345 so I thought it's √100+√n+√100-√n I thought it looked like A^2-B^2=(a+b)(a-b) √100^2-√N^2 But there's a fatal flaw two actually THERE IS NO MULTIPLICATION IN THE ORIGINAL ONE AND THERES A ROOT OVER THE ROOT

[@ZDTF]

@@drpkmath12345 Cool video btw

[@elix3085]

or 0

[@domedebali632]

You dont know what a positive integer means?

[@elix3085]

@@domedebali632 tks didnt read the question properly just skipped to the end.😁

[@Quest3669]

I got √n= 96 answer .... N its true

[@domedebali632]

What is n then? You did not get an answer but made an equation

[@Quest3669]

@domedebali632 use ur sense. n = 96^2= 9216

[@iqtrainer]

@@Quest3669You use ur sense. Get an answer if you need to. You dont have any sense

[@iqtrainer]

@@Quest3669Plus, you got a wrong answer. You are senseless animal

[@drpkmath12345]

Haha Quest that guy doesnt have sense anyway 👍👍