Let $\mathrm{a}0$. If the function $\mathrm{f}(\mathrm{x})=6{\mathrm{x}}^{3}-45{\mathrm{ax}}^{2}+108{\mathrm{a}}^{2}\mathrm{x}+1$ attains its local maximum and minimum values at the points ${\mathrm{x}}_{1}$ and ${x}_{2}$ respectively such that ${\mathrm{x}}_{1}{\mathrm{x}}_{2}=54$, then $\mathrm{a}+{\mathrm{x}}_{1}+{\mathrm{x}}_{2}$ is equal to : [JEE Main 2025, 4 Apr (Shift 2)]

Question

Let $\mathrm{a}>0$. If the function $\mathrm{f}(\mathrm{x})=6{\mathrm{x}}^{3}-45{\mathrm{ax}}^{2}+108{\mathrm{a}}^{2}\mathrm{x}+1$ attains its local maximum and minimum values at the points ${\mathrm{x}}_{1}$ and ${x}_{2}$ respectively such that ${\mathrm{x}}_{1}{\mathrm{x}}_{2}=54$, then $\mathrm{a}+{\mathrm{x}}_{1}+{\mathrm{x}}_{2}$ is equal to : [JEE Main 2025, 4 Apr (Shift 2)]

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Let \(\mathrm{a}>0\). If the function \(\mathrm{f}(\mathrm{x})=6{\mathrm{x}}^{3}-45{\mathrm{ax}}^{2}+108{\mathrm{a}}^{2}…

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