Question
If (x – 12) 3 + (x – 5) 3 +
(x – 7) 3 = 3(x – 12)(x – 5)(x – 7) then find the value of (x 2 + 5x + 12)Solution
Let a = (x – 12), b = (x – 5) and c = (x – 9)
According to the question,
a 3 + b 3 + c 3 = 3abc
Therefore, a + b + c =0
Or, x – 12 + x – 5 + x – 7 = 0
Or, 3x = 24
Or, x = 8
Therefore, x 2 + 5x + 3 = 8 2 + 5 × 8 + 12 = 116
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