Question
If x2 – xy + y2 = 16 and
x4 + x2y2 + y4 = 320 then find x2 + xy + y2 = ?Solution
Given that x2 – xy + y2 = 16 x4 + x2 y2 + y4 = 320 in equation we add and subtract x2 y2 x4 + y4+ x2 y2 + x2 y2 – x2 y2 = 320 (x2 + y2)2 – (xy)2 = 320 (x2 + y2 – xy) (x2 + y2 + xy) = 320 By using [a2 – b2 = (a + b)(a – b)] 16 × ( x2 + y2 + xy) = 320 x2 + y2 + xy = 20Â
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