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If a, b, c are in A.P., prove that: a3 + c3 + 6abc = 8b3 |
Answer» a3 + c3 + 6abc = 8b3 a3 + c3 - (2b)3 + 6abc = 0 a3 + (-2b)3 + c3 + 3a(-2b)c = 0 Since, If a + b + c = 0, a3 + b3 + c3 = 3abc (a - 2b + c)3 = 0 a - 2b + c = 0 Since, a, b, c are in AP b - a = c - b = a + c - 2b = 0 Hence proved |
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