x+y=a and xy=b then the value of 1/x^3+1/y^3 is

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question: x+y=a and xy=b then the value of 1/x^3+1/y^3 is ?.

1/x^3 + 1/y^3 = (y^3 + x^3) / (xy)^3 = (x+y)(x^2 - xy + y^2) / b^3

= a[(x^2 - 2xy + y^2) + xy] / b^3 = a(a^2 + b) / b^3

Answer: a(a^2 + b) / b^3

by Level 11 User (81.5k points)

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