Let $x, y > 0 . I f x^{3} y^{2} = 2^{15},$ then the least value of $3 x + 2 y$ is

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answer is D.

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Detailed Solution

$A M \geq G M ∴ \frac{x + x + x + y + y}{5} \geq {(x^{3} \cdot y^{2})}^{\frac{1}{5}} \Rightarrow \frac{3 x + 2 y}{5} \geq {(2^{15})}^{\frac{1}{5}} \Rightarrow 3 x + 2 y \geq 40 Least value of 3 x + 2 y i s 40$

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