Question

prove that (a-b)² , (a²+b²) and (a+b)² form an AP.

Answer 1

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Answer 2

In an AP

first term+third term=2*second term

Given first term is (a-b)²

third term =(a+b)²

first term+second term

=(a+b)²+(a-b)²

=a²+2ab+b²+a²-2ab+b²

=2a²+2b²

=2(a²+b²)

=2*2nd term

The 2nd term is a²+b²

Hence they form an AP[Proved]

Hope it helps.