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Prove that, if andΒ  be positive rationals such that, then either and or and are squares of rationals.

Answer

If , then

So, let . Then, there exists a positive rational number such that .

Now,







is rationalΒ  Β 

is the square of a rational number.

From, we have

Β 

is rational

is the square of a rational number.

Hence, either and or and are the squares of rationals.

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