Question
If (x – 12)3 + (x – 5)3 + (x
– 7)3 = 3(x – 12)(x – 5)(x – 7) then find the value of (x2 + 5x + 12)Solution
Let a = (x – 12), b = (x – 5) and c = (x – 9) According to the question, a3 + b3 + c3 = 3abc Therefore, a + b + c =0 Or, x – 12 + x – 5 + x – 7 = 0 Or, 3x = 24 Or, x = 8 Therefore, x2 + 5x + 3 = 82 + 5 × 8 + 12 = 116
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