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

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degeneratecircle's profile pic

degeneratecircle | High School Teacher | (Level 2) Associate Educator

Posted on

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)` 

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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`

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vaaruni | High School Teacher | (Level 1) Salutatorian

Posted on

Given:- (x-1/x)=4 We require to find (x+1/x) Using the formula : (a-b)^2= (a+b)^2 - 4.a.b (x-1/x)^2 = (x+1/x)^2 - 4.x.(1/x) => (x-1/x)^2 = (4)^2- 4 => (x-1/x)^2 = 16-4 =12 => (x-1/x)= sqrt(12)= sqrt(4*3)= 2*sqrt(3) => (x-1/x)= 2*1.732 [sqrt(3)=1.732] => (x-1/x)= 3.464 Hence, (x-1/x)=3.464 <-- Answer

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