Let a>0. If the function f(x)=6x³-45a x²+108a²x+1 attains its local maximum and minimum values at the points x₁ and x₂ respectively such that x₁x₂=54, then a+x₁+x₂ is equal to:

Limit, Continuity and Differentiability: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q101

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

a>0

. If the function

f(x)=6x^{3}-45a x^{2}+108a^{2}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

a+x_{1}+x_{2}

is equal to: