Question
If (5x + 2)3 + (x – 1)3 + 8(3x
– 7)3 = 6(5x + 2) × (x – 1) × (3x – 7), then the value of (5x + 3) isSolution
If a + b + c = 0, then a3 + b3 + c3 = 3abc Since, (5x + 2)3 + (x – 1)3 + 8(3x – 7)3 = (5x + 2)3 + (x – 1)3 + {2(3x – 7)3} = 3 × 2(3x – 7) × (x – 1) × (5x + 2) So, (5x + 2) + (x – 1) + 2(3x – 7) = 0 Or, 5x + 2 + x – 1 + 6x – 14 = 0 Or, 11x – 11 = 0 So, x = 1 So, 5x + 3 = 5 × 1 + 3 = 8
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