Question

if the mean √x and 1/√x is M then the mean of X^2 and 1/X^2 is

Answer 1

{√x +1/√x} /2 = M

Squaring both the sides

x+1/x +2 = 4M
or x+1/x = 4M -2

Again squaring both the sides

x² + 1/x² +2 = 4M² +4 - 16M
or x²+ 1/x² = 4M² +2 -16M
or { x²+1/x²}/2 = 2M² -8M +1. , Which is the required mean