Question

If $\frac{a}{b}+\frac{b}{a}=-1$ then (a³ − b³) = ?
(a) −3
(b) −2
(c) −1
(d) 0

Answer 1

$$\begin{gathered} \frac{a}{b}+\frac{b}{a}=-1 \\ \Rightarrow \frac{a^2+b^2}{ab}=-1 \end{gathered}$$
$\Rightarrow a$² + b² = $-$ab
$\Rightarrow a$² + b² + ab = 0

Thus, we have:
$\left(a^3-b^3\right)=\left(a-b\right)\left(a^2+b^2+ab\right)$
$$\begin{gathered} =\left(a-b\right)\times 0 \\ =0 \end{gathered}$$