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

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

Question

(C) Given that the average of $x$ and $\frac{1}{x}$ is $M$.$\frac{x + \frac{1}{x}}{2} = M$Multiplying both sides by $2$,we get:$x + \frac{1}{x} = 2M$N

Vedclass · Accepted Answer

$2M^{2}-1$

Vedclass · Answer

(C) Given that the average of $x$ and $\frac{1}{x}$ is $M$.$\frac{x + \frac{1}{x}}{2} = M$Multiplying both sides by $2$,we get:$x + \frac{1}{x} = 2M$Now,we need to find the average of $x^{2}$ and $\frac{1}{x^{2}}$,which is given by:$	ext{Average} = \frac{x^{2} + \frac{1}{x^{2}}}{2}$Using the algebraic identity $(a + b)^{2} = a^{2} + b^{2} + 2ab$,we can write:$x^{2} + \frac{1}{x^{2}} = (x + \frac{1}{x})^{2} - 2(x)(\frac{1}{x}) = (x + \frac{1}{x})^{2} - 2$Substituting the value of $(x + \frac{1}{x}) = 2M$:$x^{2} + \frac{1}{x^{2}} = (2M)^{2} - 2 = 4M^{2} - 2$Therefore,the required average is:$\frac{4M^{2} - 2}{2} = 2M^{2} - 1$

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

Out of nine persons,$8$ persons spent $Rs. 30$ each for their meals. The ninth person spent $Rs. 20$ more than the average expenditure of all the nine. What was the total money spent by all of them (in $Rs.$)?

Three years ago,the average age of a family of $5$ members was $17$ years. $A$ baby having been born,the average age of the family is the same today. The present age of the baby is (in years):

The average monthly salary of $20$ employees in an organisation is $Rs. 1500$. If the manager's salary is added, then the average salary increases by $Rs. 100$. What is the manager's monthly salary (in $Rs.$)?

The average of the first nine prime numbers is

There are $6$ consecutive odd numbers in increasing order. The difference between the average of the squares of the first $4$ numbers and the last $4$ numbers is $64$. If the sum of the squares of the first and the last element is $178$,then the average of all the $6$ numbers is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module