anonymous
  • anonymous
Prove that :If a,b belongs to Z then (a^2 + b^2)/(1 + ab) is a perfect square.
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
I know the answer......I just want to confirm it.
anonymous
  • anonymous
a = 2, b =1 \[\frac{4 + 1}{1 +2} = \frac{5}{3}\]
anonymous
  • anonymous
Or, I didn't understand your question? I don't think you will ever get a perfect square through that equation.

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anonymous
  • anonymous
Try b = 0 you get one . Now how do I prove it?
anonymous
  • anonymous
This is an IMO Problem.
anonymous
  • anonymous
But I think that's it, it's only valid when b=0. Do you have any other example?
anonymous
  • anonymous
\[\frac{a^2+b^2}{1+ab} = q^2\] \[\sqrt{\frac{a^2+b^2}{1+ab}} = q\]Now we need some manipulation here.

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