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Question Number 190942 by mathlove last updated on 14/Apr/23

$$(x+y)(x^2-xy+y^2)=2$$$$\frac{x^3{y}^3}{x^9+y^9-8}=?$$

Answered by Frix last updated on 15/Apr/23

$$x^3+y^3=2\Rightarrow y^3=2-x^3$$$$\frac{x^3(2-x^3)}{x^9+{(2-x^3)}^3-8}=\frac{x^3(2-x^3)}{-6x^3(2-x^3)}=-\frac{1}{6}$$

Answered by manxsol last updated on 15/Apr/23

$$x^3+y^3=2$$$${(x^3+y^3)}^3=x^9+y^9+3x^3{y}^3(x^3+y^3)$$$$8=x^9+y^9+6x^3{y}^3$$$$-6x^3{y}^3=x^9+y^9-8$$$$\frac{x^3{y}^3}{-6x^3{y}^3}=-\frac{1}{6}$$

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