GATE 2023 EC Q.45: official answer

Let a frequency modulated (FM) signal $x(t)=A\cos \left({\omega }_{c}t+k_f{\int }_{-\infty }^{t}m(\lambda )d\lambda \right)$, where $m(t)$ is a message signal of bandwidth $W$. It is passed through a non-linear system with output $y(t)=2x(t)+5(x(t){)}^2$. Let $B_T$ denote the FM bandwidth. The minimum value of ${\omega }_c$ required to recover $x(t)$ from $y(t)$ is