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