Question
If a, b, c are in geometric progression and a + b + c =
14, a² + b² + c² = 84, find a, b, c.Solution
ATQ,
Let a = x, b = xr, c = xr² Sum: x(1 + r + r²) = 14 Squares: x²(1 + r² + r⁴) = 84 Divide 2nd by (1st)²: (1 + r² + r⁴)/(1 + r + r²)² = 84/14² = 84/196 = 3/7 Try r = 2 → (1+4+16)/(1+2+4)² = 21/49 = 3/7 ✅ Then x(7) =14 ⇒ x = 2 → (a,b,c) = (2,4,8)
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