If x4 + x2y2 + y4 = 133 and x2 - xy + y2 = 7, then what is the value of xy?
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Correct answer: B
Explanation
The correct answer is Option 2 i.e. 6
x4 + x2y2 + y4 = 133
x2 - xy + y2 = 7
Taking square of second equation:
⇒ (x2 - xy + y2)2 = 49
⇒ x4 + x2y2 + y4 + 2(-x3y - y3x + x2y2) = 49
⇒ 133 - 2xy(x2 - xy + y2) = 49
⇒ 14xy = 133 - 49
⇒ xy = 6