If $\frac{a}{b}+\frac{b}{a}=1$, then the value of $a^3+b^3$ is

The correct option is D: $0$

Given that,

$\frac{a}{b}+\frac{b}{a}=1$

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

$\Rightarrow a^2+b^2=ab$

$\Rightarrow a^2+b^2-ab=0\dots \dots \left(i\right)$

Now, Using the identity, $a^3+b^3=(a+b)(a^2+b^2-ab)$

$=(a+b)\left(0\right)\left[\text{Using}\right(i\left)\right]$

$=0$