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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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