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    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)
    A 116 Correct Answer Incorrect Answer
    B 96 Correct Answer Incorrect Answer
    C 88 Correct Answer Incorrect Answer
    D 72 Correct Answer Incorrect Answer

    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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