Question

If `x^4+1/x^4=119, "find"  x-1/x`

Answer 1

Here, `x^4 + 1/x^4 = 119,`

Let, a = `x - 1/x`

We know that,

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

`∴x^2 + 1/x^2 = a^2 + 2`

Also,

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

Let’s try to substitute the equation. match the given equation,

We assume that a = 3,

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

`x^2 + 1/x^2 = 3^2 + 2`

`x^2 + 1/x^2 = 9 + 2`

∴ `x^2 + 1/x^2 = 11`

Then we will substitute the value of `x^2 + 1/x^2 = 11` in,

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

`x^4 + 1/x^4 = 11^2 - 2`

`x^4 + 1/x^4 = 121 - 2`

∴ `x^4 + 1/x^4 = 119`

The assumed value a = 3 provides the exact given equation, which is `x^4 + 1/x^4 = 119`

Hence, `x - 1/x = 3`