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if x-y=6 and x^2+y^2=24, find x^3-y^3

 Dec 14, 2021
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(x - y)^2 = x^2 - 2xy + y^2 => 2xy = x^2 + y^2 - (x - y)^2 => 2xy = 24 - 6^2 = -12 => xy = -6

x^3 - y^3 = (x - y) (x^2 + x y + y^2) = 6( 24 - 6 ) = 108

 Dec 14, 2021

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