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यदि x तथा `(1)/(x)(xne0)` का औसत M है, तब `x^(2)` एव `(1)/(x^(2))` का औसत ज्ञात करे ?A. `1-M^(2)`B. `1-2M^(2)`C. `2M^(2)-1`D. `2M^(2)+1` |
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Answer» Correct Answer - C 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` |
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