Question
If x3 + y3 = 9 and x + y=3 then
the value of x4 + y4 is:Solution
x3 + y3 = (x + y)(x2 – xy + y2) ⇒ 9 = 3*{(x + y)2−3xy}=3*(9−3xy) = 27−9xy Or xy=2 x2 + y2 = (x + y)2 – 2xy = 9 – 2*2 = 5 x4 + y4 = (x2 + y2)2 – 2x2y2 ⇒ x4 + y4 = 25 – 2*(2)2 = 25 – 8 = 17
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