Mathematics - Application of Derivative Question with Solution | TestHub

Let $\mathrm{a}>0$. If the function $\mathrm{f}(\mathrm{x})=6{\mathrm{x}}^3-45\mathrm{a}{\mathrm{x}}^2+108{\mathrm{a}}^2\mathrm{x}+1$ attains its local maximum and minimum values at the points $x_1$ and $x_2$ respectively such that $x_1{x}_2=54$, then $\mathrm{a}+{\mathrm{x}}_1+{\mathrm{x}}_2$ is equal to :-