QJEEM22Ma4279: JEE Main 2022 Mathematics - Class 11 JEEM22Ma4279 Solution: Let x, y > 0. If x 3 y 2 = 2 15 , then the least value of 3x +…

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Let x, y > 0. If x³y² = 2¹⁵, then the least value of 3x + 2y is

Accepted Answer

x, y > 0 and x³y² = 2¹⁵

Now, 3x + 2y = (x + x + x) + (y + y)

So, by A.M $\ge$ G.M inequality

$\frac{3 x + 2 y}{5} \geq \sqrt[5]{x^{3} . y^{2}}$

$\therefore$ $3 x + 2 y \geq 5 \sqrt[5]{2^{15}} \geq 40$

$\therefore$ Least value of $3x + 4y = 40$

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