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    Question

    If (x 4  + x 2 y 2  +

    y 4 ) = 216 and (x 2  - xy + y 2 ) = 12, then find the value of '3xy'.
    A 12 Correct Answer Incorrect Answer
    B 3 Correct Answer Incorrect Answer
    C 6 Correct Answer Incorrect Answer
    D 9 Correct Answer Incorrect Answer

    Solution

    x 2  - xy + y 2  = 12 -------- (I)

    Using, (x 4  + x 2 y 2  + y 4 ) = (x 2  - xy + y 2 ) (x 2  + xy + y 2 )

    216 = 12 X (x 2  + xy + y 2 )

    Or, x 2  + xy + y 2  = 18 -------- (II)

    On subtracting equation (II) from (I) ,

    We get, x 2  - xy + y 2  - (x 2  + xy + y 2 ) = 12 - 18

    Or, x 2  - xy + y 2  - x 2  - xy - y 2  = - 6

    Or, 2xy = 6

    Or, xy = 3

    Required value = 3 X 3 = 9

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