Question

Mean of x and 1/x is k, then find the mean of x^2 and 1/x^2 . Explain it neately

Answer 1

by given,
$\frac{x+ \frac{1}{x} }{2}$  =k
thus,x+$\frac{1}{x}$=2k
x²+$\frac{1}{ x^{2} }$=(x+$\frac{1}{x}$)²-2
                                             =4k²-2
so,their mean is  4k²-2/2