Question

If the product of two positive numbers is $256$ then the least value of their sum is

• A. $32$
• B. $16$
• C. $48$
• D. $40$

Answer 1

The correct option is A $32$

$xy=256$
$s=x+y$
$s=x+\frac{256}{x}$
use AM & GM
$\frac{x+\frac{256}{x}}{2}\ge (x\times \frac{256}{x}{)}^{\frac{1}{2}}$
$x+\frac{256}{x}\ge 32$