Question

6. Prove that if x and y are odd positive integers, then x² + y² is even but not divisible by 4.

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Answer 1

Answer>=====================================

we know that, sum of two odd positive number is even positive number ,

So, x+y = 2q ( even no. is of the form 2q)

(x+y)² = (2q)²

x² + y²+ 2xy = 4q²

x² + y ² = 4q² -2x

x² + y² = 2( 2q²- x)

clearly, x²+ y² is divisible by 2

But it is not having 4 as its factor,

Hence, x²+ y² is even but not divisible by 4.

Proved.....

Thankyou , hope you got it.

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