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    Question

    If (x + y + z) = 10 and (x 2  + y 2

     + z 2 ) = 52, then find {z(x + y) + xy}.
    A 36 Correct Answer Incorrect Answer
    B 32 Correct Answer Incorrect Answer
    C 48 Correct Answer Incorrect Answer
    D 24 Correct Answer Incorrect Answer

    Solution

    Since, (x + y + z) 2  = x 2  + y 2  + z 2  + 2(xy +yz +zx)

    So, (10) 2   = 52 + 2(xy +yz +zx)

    Or, 100 - 52 = 2(xy +yz +zx)

    Or, 48 = 2(xy +yz +zx)

    Or, 24 = (xy +yz +zx)

    So, z(x + y) + xy = 24

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