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    Question

    If x + y + z = 9 and xy + yz + zx = 26, find the value

    of x³ + y³ + z³ − 3xyz.
    A 52 Correct Answer Incorrect Answer
    B 40 Correct Answer Incorrect Answer
    C 33 Correct Answer Incorrect Answer
    D 27 Correct Answer Incorrect Answer

    Solution

    ATQ, Use identity: x³ + y³ + z³ − 3xyz = (x + y + z)[x² + y² + z² − xy − yz − zx] First, x² + y² + z² = (x + y + z)² − 2(xy + yz + zx) = 9² − 2×26 = 81 − 52 = 29 Then: x² + y² + z² − xy − yz − zx = 29 − 26 = 3 So: x³ + y³ + z³ − 3xyz = (x + y + z) × 3 = 9 × 3 = 27.

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