Question

The sum of two numbers is 6. The minimum value of the sum of their reciprocals is

• A. $\frac{3}{4}$
• B. $\frac{6}{5}$
• C. $\frac{2}{3}$
• D. $\frac{2}{5}$

Answer 1

The correct option is C $\frac{2}{3}$

$x+y=6$
$Sum=\frac{1}{x}+\frac{1}{y}$
$\frac{d\left(sum\right)}{dx}=\frac{-1}{x^2}+\frac{1}{(6-x{)}^2}=0$
$x^2=(6-x{)}^2$
$x=\pm (6-x)$
$x=3$, $y=3$
$Sum=\frac{2}{3}$