Question

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

• A. 30
• B. 32
• C. 36
• D. 40

Answer 1

Answer: (D)

40

Answer 2

$x, y > 0$ and $x^3y^2 = 2^{15}$

Now,

$3x+2y = (x+x+x)+(y+y)$

So, by A.M G.M inequality

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

$∴ \; 3x+2y \geq 55\sqrt{2^{15}}$

$≥40$

$∴$ Least value of $3x + 4y = 40$

Therefore, the correct option is (D): $40$