Question 29

If xy(x+y)=1 then, the value of $$\frac{1}{x^{3}y^{3}}-x^{3}-y^{3}$$ is

Solution

xy(x+y)=1

x+y = 1/xy

apply cube on both sides,

$$(x+y)^{3}$$ = $$\frac{1}{x^{3}y^{3}}$$

$$x^{3}+y^{3}+3xy(x+y)$$ = $$\frac{1}{x^{3}y^{3}}$$

$$x^{3}+y^{3}+3(1)$$ = $$\frac{1}{x^{3}y^{3}}$$

3 = $$\frac{1}{x^{3}y^{3}}$$ - $$x^{3}-y^{3}$$

so the answer is option A.

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