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  4. Let x, y > 0. If x3 y2=215, then the least value of 3 x +2 y is

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

JEE MainJEE Main 2022Permutations and Combinations

Solution:

Using $A M \geq G M$
$\frac{x+x+x+y+y}{5} \geq\left(x^{3} \cdot y^{2}\right)^{\frac{1}{5}} $
$\frac{3 x+2 y}{5} \geq\left(2^{15}\right)^{\frac{1}{5}}$
$(3 x+2 y)_{\min }=40$