Question

If $x+y=a$ and $xy=b$, then the value of $\frac{1}{x^3}+\frac{1}{y^3}$ is equal to

• A. $a^3-3ab$
• B. $\frac{a^3-3ab}{b^3}$
• C. $\frac{a^3+3ab}{b^3}$
• D. $a^3+3ab$

Answer 1

The correct option is B $\frac{a^3-3ab}{b^3}$

$\frac{1}{x^3}+\frac{1}{y^3}=\frac{x^3+y^3}{x^3{y}^3}=\frac{(x+y{)}^3-3xy(x+y)}{(xy{)}^3}$
$=\frac{a^3-3ba}{b^3}=\frac{a^3-3ab}{b^3}$