Question

If \[x + \frac{1}{x}\] 4, then \[x^4 + \frac{1}{x^4} =\]

Options

• 196

• 194

• 192

• 190

Answer 1

In the given problem, we have to find the value of  `x^4 + 1/x^4`

Given  `x+ 1/x = 4`

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

Here put,`x+ 1/x = 4`

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

             `(4)^2 = x^2 + 1/x^2 + 2 (x xx 1/x )`

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

           ` 16 -2 = x^2 + 1/x^2`

                 `14 = x^2 + 1/x^2`

Squaring on both sides we get, 

`(14)^2 = (x^2 + 1/x^2 )^2`

`14 xx 14 = (x^2)^2 + (1/x^2) ^2 + 2 xx x^2 xx 1/x^2`

       `196 = x^4 + 1/x^4 + 2`

`196 -2 = x^4 + 1/x^4`

       `194= x^4 + 1/x^4`

Hence the value of  `x^4 + 1/x^4`is 194.