Question
If x4 + x2 y2 +
y4 = 37 and x2 – xy + y2 = 5, then what is the value of xy ?Solution
x4 + x2 y2 + y2 = 37 and x2 – xy + y2 = 5 --- (1) As we know, (x4 + x2 y2 + y2) = (x2 – xy + y2) (x2 + xy + y2) ⇒ x2 + xy + y2 = 37/5 ⇒ x2 – xy + y2 = 7.4 --- (2) Subtract equation (2) from equation (1) ⇒ 2xy = 2.4 ⇒ xy = 1.2
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