If the average of x and frac{1}{x}(x neq 0) i | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

Average of $x$ and $\frac{1}{x}=m$

$\Rightarrow \frac{x+\frac{1}{x}}{2}=m \Rightarrow x+\frac{1}{x}=2 m$

Now $x^{2}$ and $\frac{1}{x^{2}}$

$\

Vedclass · Accepted Answer

$2 M ^{2}-1$

Vedclass · Answer

Average of $x$ and $\frac{1}{x}=m$

$\Rightarrow \frac{x+\frac{1}{x}}{2}=m \Rightarrow x+\frac{1}{x}=2 m$

Now $x^{2}$ and $\frac{1}{x^{2}}$

$\Rightarrow \frac{x^{2}+\frac{1}{x^{2}}}{2}=\frac{\left(x+\frac{1}{x}\right)^{2}-2}{2}=\frac{4 m^{2}-2}{2}=2 m^{2}-1$

If the average of $x$ and $\frac{1}{x}(x \neq 0)$ is $M,$ then the average of $x^{2}$ and $\frac{1}{x^{2}}$ is

Similar Questions

The average age of $6$ members of a family is $20\, years.$ If the age of a servant is included, the average age increased by $25 \%$. What is the age (in $years$) of the servant ?

The average score of Sachin after $25$ innings is $46$ runs per innings. If after the $26^{th}$ innings, his average runs increased by $2$ runs, then what is his score in the $26^{\text {th }}$ innings?

In a school with $600$ students, the average age of the boys is $12$ $years$ and that of the girls is $11\, years.$ If the average age of the school is $11 \,years$ and $9 \,months,$ then the number of girls in the school is

The average of five numbers is $6.9 .$ If one of the numbers is deleted, the average of the remaining numbers is $4.4 .$ What is the value of the number deleted?

Average age of $5$ boys is $16$ $year$ of which that of $4$ boys is $16\, year\, 3\, months.$ The age of the $5^{th}$ boy is