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If a, b, c are in A.P., prove that: (a - c)2 = 4 (a - b) (b - c) |
Answer» (a - c)2 = 4 (a - b) (b - c) a2 + c2 - 2ac = 4(ab – ac – b2 + bc) a2 + 4c2b2 + 2ac - 4ab - 4bc = 0 (a + c - 2b)2 = 0 a + c - 2b = 0 Since, a, b, c are in AP b - a = c - b a + c - 2b = 0 Hence, (a - c)2 = 4 (a - b) (b - c) |
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