China | A Nice Algebra Problem | Math Olympiad

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Find the value of x and y?
How to solve √2^ √x - √2^√y = 28
In this video, we'll show you How to Solve Math Olympiad Question A Nice Radical Equation √2^ √x - √2^√y = 28 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 #maths #math #algebra

[@LITHICKROSHANMS-gw2lx]

Very nice sir!

[@SALogics]

Thanks for liking. ❤

[@SGuerra]

Bela questão! Parabéns pela escolha!

[@SALogics]

muito obrigado!

[@YAWTon]

This is a very easy problem: (x,y) = (x, 4*(ld(2^(√2/2)+28)^2) are the infinitely many real solutions. Did you forget to say that you are looking for integer solutions? There is an obvious integer solution if you use the substitution m=√x/2 and n=√y/2, since 28=32-4=2^5-2^2 --> x=100, y=16.

[@SALogics]

Very nice! ❤

[@haticekoca5716]

2^x-2^y=28 28=7,4 2^4-2^7 2^4= 16 2^7=128-28= 100 x=100 y=16

[@SALogics]

Very nice trick! ❤

[@YAWTon]

You are assuming that m and n in your solution are positive integers.Can you justify this assumption? If you are interested in integer solutions x, y: from x, y integer it does not follow that m and n are integer too.

[@SALogics]

If x and y are positive integers then m and are also positive integers. ❤

[@YAWTon]

Prove it! From m=√x/2 it does not follow that m is an integer. Example:if x=2 then m is √2/2 which is NOT an integer.

[@SALogics]

@@YAWTon You are right! m and n can only be integers when x and y are perfect squares and Even numbers. Sorry for inconvenience! ❤

[@YAWTon]

@@SALogics No inconvenience at all! I'm just wondering if you have a proof that (100,16) is the only integer solution. I do not have a proof (yet), but I think that there is only one integer solution. And of course there are infinitely many real solutions

[@sandytanner9333]

X=100 y=16

[@SALogics]

Yes, you are right! ❤