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Algebraic Identities

Find x3 + y...

Question

Find $x^{3} + y^{3}$ if $x + y = 4$ and $x y = 5$

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Solution

We know that $x^{3} + y^{3} = (x + y)^{3} - 3 x y (x + y)$
$∴ x^{3} + y^{3} = (4)^{3} - 3 (5) (4) = 64 - 60 = 4$

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