Question

If the mean of x and1/x is M then prove that mean of x square and1/xsquare is 2msquare - 1

Answer 1

(X+1/X)^2=X square +1/xsquare +2
given X+1/X=2M
so on squaring both side
x^2 +1/x^2+2=4Msquare
x^2+1/x^2=4 M square -2
so mean of
(xsquare +1/X square )/2=2Msquare -1