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