MCQ
If $\frac{\text{a}}{\text{b}}+\frac{\text{b}}{\text{a}}=-1,$ then $a^3 - b^3=$
- A$1$
- B$-1$
- C$\frac{1}{2}$
- ✓$0$
✓
Answer
Correct option: D.
$0$
$\frac{\text{a}}{\text{b}}+\frac{\text{b}}{\text{a}}=-1$
$\Rightarrow\frac{\text{a}^2+\text{b}^2}{\text{ab}}=-1$
$\Rightarrow\text{a}^2+\text{b}^2+\text{ab}=0$
Now using identity
$a^3-b^3$
$=(a-b)\left(a^2+b^2+a b\right)$
$=(a-b)(0)\left(\because a^2+b^2+a b=0\right)$
$=0$
Hence, correct option is $(d).$
$\Rightarrow\frac{\text{a}^2+\text{b}^2}{\text{ab}}=-1$
$\Rightarrow\text{a}^2+\text{b}^2+\text{ab}=0$
Now using identity
$a^3-b^3$
$=(a-b)\left(a^2+b^2+a b\right)$
$=(a-b)(0)\left(\because a^2+b^2+a b=0\right)$
$=0$
Hence, correct option is $(d).$
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