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anonymous
 4 years ago
Prove that :If a,b belongs to Z then (a^2 + b^2)/(1 + ab) is a perfect square.
anonymous
 4 years ago
Prove that :If a,b belongs to Z then (a^2 + b^2)/(1 + ab) is a perfect square.

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I know the answer......I just want to confirm it.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0a = 2, b =1 \[\frac{4 + 1}{1 +2} = \frac{5}{3}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Or, I didn't understand your question? I don't think you will ever get a perfect square through that equation.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Try b = 0 you get one . Now how do I prove it?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0This is an IMO Problem.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0But I think that's it, it's only valid when b=0. Do you have any other example?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\frac{a^2+b^2}{1+ab} = q^2\] \[\sqrt{\frac{a^2+b^2}{1+ab}} = q\]Now we need some manipulation here.
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