Question

If the mean of x and 1/x is M, then the mean of x^ and 1/x^2
is :

(A)M^2

(B)M^2/4

(C)2M^2-1

(D) 2M^2+1

Please make process ways
I will mark as brainliest.
so,please fast​

Answer 1

Required Answer

Option (C) $2M^2-1$

Before we solve

The mean of two quantities is their sum divided by 2. We can find the sum first. Then we need the power of 2, so we square on both sides. Let's start.

Solution

Given $\dfrac{1}{2}(x+\dfrac{1}{x} )=M$

$\rightarrow x+\dfrac{1}{x} =2M$

$\rightarrow (x+\dfrac{1}{x} )^2=4M^2$

$\rightarrow x^2+2\times x\times \dfrac{1}{x} +\dfrac{1}{x^2} =4M^2$

$\rightarrow x^2+2+\dfrac{1}{x^2} =4M^2$

$\rightarrow x^2+\dfrac{1}{x^2}=4M^2-2$

Hence

$\rightarrow\dfrac{1}{2} (x^2+\dfrac{1}{x^2} )=\dfrac{1}{2} (4M^2-2)$

$\rightarrow\dfrac{1}{2} (x^2+\dfrac{1}{x^2} )=\boxed{2M^2-1}$

So, the required answer is option (C) $2M^2-1$.

Answer 2

Answer:

Given,

The mean of x and 1/x is M

then M= x+1/x /2 =M

= 2M=x+1/x

square both these side

ஃ (x+1/x)^2=(2M)^2 =x^2+(1/x)^2

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

The mean of x^2 and 1/x^2

x^2+1/x^2/2 = 4M^2+2

= x^2+1/x = 2M+1