Question

if the average of x and y is 11/2 and the average of 1/x and 1/y is 11/24, then xy=

Answer 1

Given the average of $x$ and $y$.

$\frac{x+y}{2} =\frac{11}{2}$ .........................(1)

Also given the average of $\frac{1}{x}$ and $\frac{1}{y}$.

$\frac{1/x+1/y}{2} =\frac{11}{24} \\ \frac{x+y}{2xy} =\frac{11}{24}$ .........................(2)

Combining the two equations (1) and (2),

$\frac{\frac{11}{2}}{2xy} =\frac{11}{24}\\ \frac{11}{4xy} =\frac{11}{24}\\ xy=6$