यदि x तथा `(1)/(x)(xne0)` का औसत M है, तब `x^(2)` एव `(1)/(x^(2))` का औसत ज्ञात करे ?

Options

A. `1-M^(2)`
B. `1-2M^(2)`
C. `2M^(2)-1`
D. `2M^(2)+1`

Answer

C

Explanation

According to question
Average of `(x+1/x)/2` =M
put x = 1
`therefore (1+1/1)/2` M
M=1
`therefore (x^2+1/x^2)/2=(1^2+1/1^2)/2`=1
Now check from the option : (c ) `2M^2 - 1` (put M=1)
2 x 1 - 1 =1 (Satisfied )
Alternate:
According to question
`(x+1/x)/2=M`
`(x+1/x)=2M`
`therefore x^2+1/x^2=(2M)^2-2=4M^2-2`
Required average = `(x^2+1/x^2)/2`
`=(4M^2-2)/2=2M^2-1`