Question
If (x 4 + x 2 y 2 +
y 4 ) = 216 and (x 2 - xy + y 2 ) = 12, then find the value of '3xy'.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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