Question

Mark the correct alternative in each of the following:

If \[x + \frac{1}{x} = 5\] then \[x^2 + \frac{1}{x^2} = \]

पर्याय

• 25

• 10

• 23

• 27

Answer 1

In the given problem, we have to find the value of  `x^2 + 1/x^2 `

Given  `x+ 1/x = 5`

We shall use the identity `(a+b)^2 = a^2 + b^2 + 2ab`

Here put `x+1/x = 5`

`(x+1/x)^2 = x^2 +1/x^2 +2 (x xx 1/x)`

             `(5)^2 = x^2 + 1/x^2 +2 (x xx 1/x)`

                `25 = x^2 + 1/x^2 + 2`

          `25 - 2 = x^2 +1/x^2`

                `23 = x^2 + 1/x^2`

Hence the value of   `x^2 + 1/x^2` is 23.