Question
If a, b, c are in geometric progression and a + b + c =
14, aĀ² + bĀ² + cĀ² = 84, find a, b, c.Solution
ATQ,
Let a = x, b = xr, c = xrĀ² Sum: x(1 + r + rĀ²) = 14 Squares: xĀ²(1 + rĀ² + rā“) = 84 Divide 2nd by (1st)Ā²: (1 + rĀ² + rā“)/(1 + r + rĀ²)Ā² = 84/14Ā² = 84/196 = 3/7 Try r = 2 ā (1+4+16)/(1+2+4)Ā² = 21/49 = 3/7 ā Then x(7) =14 ā x = 2 ā (a,b,c) = (2,4,8)
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