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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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