The answer above is correct, but a little hard to read and only gets one solution. I'll do something similar. It's a much easier way to do it than using the quadratic formula, which I think is the first thing most people would try.
First, note that
`(x+1/x)^2=16,` since `x+1/x=4.` So we get
`16=x^2+1/(x^2)+2,` or in other words, `14=x^2+1/(x^2).` Plug this in to our first equation to get
`(x-1/x)^2=14-2=12,` so we get the two solutions
It is given that `x + 1/x = 4` .
`x + 1/x = 4`
=> `1/x = 4 - x`
`x - 1/x`
= `x - (4 - x)`
=> `x - 4 + x`
=> `2x - 4`
Given that `x + 1/x = 4` , `x - 1/x = 2x - 4`