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.
$0$
$\frac{\text{a}}{\text{b}}+\frac{\text{b}}{\text{a}}=1\Rightarrow\text{a}^2+\text{b}^2-\text{ab}=0$
Now by identity $a^3+b^3=(a+b)\left(a^2+b^2-a b\right)$.
if $a^2+b^2-a b=0$.
then $a^3+b^3=0$
Hence, correct option is $(d)$.
Now by identity $a^3+b^3=(a+b)\left(a^2+b^2-a b\right)$.
if $a^2+b^2-a b=0$.
then $a^3+b^3=0$
Hence, correct option is $(d)$.
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