Question

if the mean of X and 1 by X is and then find the mean of x square + 1 by x square question 4plz

Answer 1

Solution:

Given:
The mean of x and $\frac{1}{x}$ is M,.
It means,

 $\frac{x+ \frac{1}{x} }{2} = M$


$\frac{ \frac{(x^2+1}{x}) }{2} = M$


$\frac{x^2+1}{x} ( \frac{1}{2} ) = M$

[tex] \frac{x^2+1}{2x} = M, [/tex] ........(i)

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To find : The value of x² and$\frac{1}{x^2}$ =?

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Mean of the numbers

=$\frac{x^2 + \frac{1}{x^2} }{2}$


=$\frac{ ( \frac{x^4 + 1}{x^2}) }{2}$


=$\frac{x^4+1}{2x^2}$ ........(ii)


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Let's compare the results with the given options,


 2M²-1 = 2($\frac{x^2+1}{2x}$)² -1

 
= 2($\frac{x^4+2x^2+1}{4x^2}$)-1


=($\frac{x^4+2x^2+1}{2x^2}$)-1$\frac{x^4+2x^2+1}{2x^2} - \frac{2x^2}{2x^2}$


=$\frac{x^4+2x^2+1-2x^2}{2x^2}$


=$\frac{x^4+1}{2x^2}$ = mean of x² and $\frac{1}{x^2}$ ,.


Hence, Option A) is correct.

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                                       Hope it Helps !!