Multiple Choice Questions on If x y z 13 and x2 y2 z2 69 then xy z x y is equal to ........ for Common University Entrance Test (CUET) Preparation

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Multiple Choice Questions

If x y z 13 and x2 y2 z2 69 then xy z x y is equal to ........

Quantitative Aptitude (CUET) Algebra
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    If x + y + z = 13 and x2 + y2 + z2 = 69, then xy + z (x + y) is equal to

    70

    Incorrect Answer

    40

    Incorrect Answer

    50

    Correct Answer

    60

    Incorrect Answer
    Explanation:

    x + y + z = 13
    x2 + y2 + z2 = 69
    (x + y + z)2 
    = x2 + y2 + z2 + 2(xy + yz + zx)
    ⇒ (13)2 = 69 + 2[xy + z(x + y)]
    ⇒ 2[xy + z(x + y)]
    = 169 – 69 = 100
    ⇒ [xy + z(x + y)] = 100/2 = 50

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