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If 2^x+2^y=x^2+y^2 where x and y are non-negative integers,it

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Joined: 02 Apr 2018
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If 2^x+2^y=x^2+y^2 where x and y are non-negative integers,it  [#permalink]

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New post 15 Apr 2018, 11:07
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If \(2^x\)+\(2^y\)=\(x^2\)+\(y^2\) where x and y are non-negative integers, what is the greatest possible value of |x−y|?

a. 0
b. 1
c. 2
d. 3
e. 4
How to solve that question

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Re: If 2^x+2^y=x^2+y^2 where x and y are non-negative integers,it  [#permalink]

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New post 23 Apr 2018, 04:28
abdelazizlila wrote:
If \(2^x\)+\(2^y\)=\(x^2\)+\(y^2\) where x and y are non-negative integers, what is the greatest possible value of |x−y|?

a. 0
b. 1
c. 2
d. 3
e. 4
How to solve that question

Posted from my mobile device


I couldn't find algebraic solution.

I picked numbers to match the answer choices

if the difference is "0" then x=y, try substituting x&y with "2" didn't work out
if the difference is "1" then x is more than y by one, try substituting x&y with "2&3" didn't work out
if the difference is "2" then x is more than y by two, try substituting x&y with "2&4" matched the given equation

Correct answer is C

However, I believe there should be a faster solution
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Re: If 2^x+2^y=x^2+y^2 where x and y are non-negative integers,it  [#permalink]

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New post 23 Apr 2018, 05:28
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Re: If 2^x+2^y=x^2+y^2 where x and y are non-negative integers,it   [#permalink] 23 Apr 2018, 05:28
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