MCQ
If $\frac{a}{b}+\frac{b}{a}=-1$ then $\left(a^3-b^3\right)=$ ?
- A$-3$
- B$-2$
- C$-1$
- ✓$0$
✓
Answer
Correct option: D.
$0$
$\frac{a}{b}+\frac{b}{a}=-1$
$\Rightarrow \frac{a^2+b^2}{a b}=-1$
$\Rightarrow a^2+b^2=-a b$
$\Rightarrow a^2+b^2+a b=0$
Thus, we have:
$\left(a^3-b^3\right)=(a-b)\left(a^2+b^2+a b\right)$
$=(a-b) \times 0$
$=0$
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