Question : If $x^4+x^2 y^2+y^4=133$ and $x^2-x y+y^2=7$, then what is the value of $xy$?
Option 1: 8
Option 2: 12
Option 3: 4
Option 4: 6
Correct Answer: 6
Solution : Given: $x^2-x y+y^2=7$ -----------(i) Also, $x^4+x^2 y^2+y^4=133$ ⇒ $(x^2-x y+y^2)(x^2+x y+y^2) = 133$ ⇒ $7(x^2+x y+y^2) = 133$ ⇒ $x^2+x y+y^2 = 19$ ------------(ii) Subtracting (i) from (ii), $2xy = 19-7$ ⇒ $xy = 6$ Hence, the correct answer is 6.
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