# If `x + 1/x = 4` then what is `x - 1/x ` equal to ? ``

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### 3 Answers

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

`(x+1/x)^2=x^2+1/(x^2)+2,` but

`(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

`x-1/x=+-sqrt(12)`

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`