Question

If x + \[\frac{1}{x}\] = then find the value of \[x^2 + \frac{1}{x^2}\].

Answer 1

We have to find the value of  `x^2 + 1/x^2 `

Given  `x+ 1/x = 3`

Using identity  `(a+b)^2 = a^2 + 2ab + b^2`

Here  `a= x,b= 1/x`

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

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

 ` (x+1/x)^2 = x^2 + 2+ 1/x^3`

By substituting the value of  `x + 1/x = 3` we get,

 `(3)^2 = x^2 + 2+ 1/x^2`

 `3 xx 3 = x^2 + 2 +1/x^2`

By transposing + 2 to left hand side, we get

`9 -2 = x^2 +1/x^2` 

       `7 = x^2 + 1/x^2`

Hence the value of  `x^2 + 1/x^2`is 7 .