A Nice Algebraic Equation | You Should Know How To Solve This!

Welcome to our channel, where we unlock the secrets of Olympiad-level mathematics! In this captivating video, we'll delve into a truly beautiful Olympiad math question that will challenge your problem-solving skills and ignite your passion for mathematics.
As we explore this exquisite problem, we'll break down its components, discuss various approaches, and provide insightful strategies to tackle it with confidence. Whether you're a seasoned math enthusiast or just starting your journey, this video offers something for everyone.
Join us as we embark on a mathematical journey filled with elegance, creativity, and intellectual stimulation. Get ready to sharpen your mathematical prowess and uncover the beauty hidden within this Olympiad math gem!
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[@869dailymathematics]

Please subscribe and like this video, let's have 100 likes

[@kiwidamien]

This assumes that x and y are positive integers, not just positive numbers. The original problem has a, b being positive numbers (not restricted to integers) but if we make the restriction that an and b are integers, the integers are not closed under square roots. When you move the square root outside the bracket, you potentially lose solutions that are in the integers

[@itodoregina5698]

Umm nice one

[@buster2256]

a missed solution is the trivial a=18 b=1

[@kiwidamien]

@@buster2256 yep, that is the assumption that you can take (a^b)^(2/2) = (a^(b/2))^2, which is a dangerous assumption in complex numbers, and just wrong in the integers.

[@mattay-gg2zt]

This problem actually has infinite solutions. Try using desmos and plugging in "x^{y}-y^{x}=17" and you'll see a very unique shape. x^{y}-y^{x}=2 looks pretty cool too

[@Roumigiere]

also 18^1 - 1^18

[@danielandreisx]

Thanks. It's always good to refresh my memory with equations like this.

[@869dailymathematics]

Glad it was helpful!

[@fonikal549]

Wonderful video sir

[@869dailymathematics]

Thanks

[@gmrachit7964]

very nice example

[@869dailymathematics]

Thanks

[@itodoregina5698]

I now understand this kind of mathematics wow you are the best math teacher i have seen

[@869dailymathematics]

I appreciate that

[@chronxdev]

This is neat, but where in the real world would you ever encounter a relation of the form a^b - b^a ??

[@carly09et]

I just choose the degenerate let b = 1 this gets a^1-1^a =17 this gives a = 18 so (a,b) ===(18,1)