1.

Show that (a – b)2, (a2 + b2) and (a + b)2 are in A.P.

Answer»

If (a – b)2, (a2 + b2) and (a + b)2 have to be in A.P. then,

It should satisfy the condition,

2b = a + c [for a, b, c are in A.P]

Thus,

2 (a2 + b2) = (a – b)2 + (a + b)2

2 (a2 + b2) = a2 + b2 – 2ab + a2 + b2 + 2ab

2 (a2 + b2) = 2a2 + 2b2 = 2 (a2 + b2)

LHS = RHS

Hence proved



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