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

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15 Apr 2018, 11:07
00:00

Difficulty:

(N/A)

Question Stats:

100% (01:19) correct 0% (00:00) wrong based on 13 sessions

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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

Posted from my mobile device
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Schools: Rotman '21
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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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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

However, I believe there should be a faster solution
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Posts: 58435
Re: If 2^x+2^y=x^2+y^2 where x and y are non-negative integers,it  [#permalink]

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23 Apr 2018, 05:28
1
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

Discussed here: https://gmatclub.com/forum/if-2-x-2-y-x ... 88016.html
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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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