Question

State whether the following statement is true or not:

If $\frac{a}{b}+\frac{b}{a}=-1$, then $a^3-b^3=0$.

• A. True
• B. False

Answer 1

The correct option is A True

Given:

$\frac{a}{b}+\frac{b}{a}=-1⟹\frac{a^2+b^2}{ab}=-1$

$⟹a^2+b^2=-ab$

$⟹a^2+b^2+ab=0$.................[1]

Now,

$a^3-b^3=(a-b)(a^2+ab+b^2)$

$=(a-b)\times 0=0$...................................[from $1$]