# What will be the Mean? If

The mean of x and 1/x is M. Then the mean of x^{2} and 1/x^{2} is:

- M
^{2 } - M
^{2}-2 - 4M
^{2}-2 - 2M
^{2}-1

**Answer: (4) 2M ^{2} – 1
Explanation:-
**Given-

(x + 1/x)/2 = M

Then, x + 1/x = 2M …………………. (1)

Square on both side of equation (1)

(x + 1/x)

^{2}= x

^{2}+ 1/x

^{2}+ 2 x X x 1/X

(2M)

^{2}= x

^{2}+ 1/x

^{2}+ 2 {from equation (1) x + 1/x = 2M }

4M

^{2}= x

^{2}+ 1/x

^{2}+ 2

4M

^{2}– 2 = x

^{2}+ 1/x

^{2}

mean of x

^{2}+ 1/x

^{2})/2 = (4M

^{2}– 2)/2

= 2M

^{2}– 1

Hence, the answer is (4) 2M^{2} – 1.