China | A Nice Algebra Problem | Math Olympiad

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Find the value of x and y?
How to solve x^y+y^x=17
In this video, we'll show you How to Solve Math Olympiad Question A Nice Exponential Equation x^y+y^x=17 in a clear , fast and easy way. Whether you are a student learning basics or a professtional looking to improve your skills, this video is for you. By the end of this video, you'll have a solid understanding of how to solve math olympiad exponential equations and be able to apply these skills to a variety of problems.
#matholympiad #mathtricks #maths

[@mrjnutube]

You could simply say:
Let a²=x^y, b²=y^x. You'll arrive at the same answer, and it'll be faster.

[@SALogics]

You are right, I appreciate your idea ❤

[@silvanomattioli9720]

3^4-4^3 easy in brute force mode like y made at the end. BUT is not the only one...

[@SALogics]

Very nice solution, I appreciate that ❤

[@BruisedReedofTas]

Method is ok until the factorization of 17 part. You're assuming solution from the Natural numbers without explicitly saying so (and that a Natural number solution won't result from a "non-Natural factorization"). As another commenter points out, expanding to the integers gives two more solutions (factorization of -1x-17 and -17x-1 are both valid). Expanding to real or complex numbers does give infinite solutions as all a = m+ni, b = 17/m-ni (m,n are any real numbers, m=/= 0) lead to valid solutions as well.

[@SALogics]

You are right, I appreciate your knowledge ❤

[@GT-fs5fu]

Nice video. Keep up the good work.

[@SALogics]

Thanks, will do! ❤

[@David2718281828]

Don't work so hard! 18^1 - 1^18 = 17

[@David2718281828]

This is similar to the solution by @user-ts9kq4vn2u

[@David2718281828]

But with one equation and two unknowns, for any given value of x you can likely find a solution for y.

[@SALogics]

Very nice, you are a genius, I appreciate that ❤

[@SALogics]

Really??

[@SALogics]

Yes, you are right ❤

[@Lemda_gtr]

Smart

[@SALogics]

Thanks and welcome ❤

[@abbasmasum1633]

The best methos ever. Guess & check is not a real method. Thank you for showing us this :)

[@SALogics]

You're welcome! ❤

[@nikolayguzman331]

Nice idea.

[@SALogics]

Thanks a lot ❤

[@santokhsidhuatla7045]

X^y-y^x= 17
3^4-4^3=17
81-64=17
X=3
Y=4

[@SALogics]

Yes, you are a genius! I appreciate that ❤

[@alfonsorafaelposadaescando4482]

Buenísimo
👍👍🇻🇪👍👍

[@SALogics]

muchas gracias! ❤
Thank you so much ❤

[@markderlo212]

I wonder if this method is applicable eg to
this : x^y - y^x = 399 ? or ...= 169