# Find x in tricky equation

1. May 29, 2012

### aaaa202

1. The problem statement, all variables and given/known data
find x in the equation:

a = x + 1/x

2. Relevant equations

3. The attempt at a solution
I sat down and thought it was easy to do, but was terribly schocked at the fact, that I didn't know how to solve this equation. What is the general approach?

2. May 29, 2012

### SammyS

Staff Emeritus
Multiplying both sides by x results in a quadratic equation.

3. May 29, 2012

### HallsofIvy

If that is 1= x+ (1/x) then multiplying both sides by x gives the quadratic equation $x= x^2+ 1$ which is equivalent to $x^2- x+ 1= 0$. You will find that it has no real roots.

If it is, rather, 1= (x+ 1)/x (in which case you should have used parentheses) you can again multiply both sides by x to get x= x+ 1 which is not true for any value of x.

Last edited by a moderator: May 30, 2012
4. May 29, 2012

### SammyS

Staff Emeritus
If a ≠ 1, then $\displaystyle a=\frac{x+1}{x}$ does have one real root.

5. May 29, 2012

### dimension10

[Post cleared by myself]

Last edited: May 29, 2012
6. May 29, 2012

### dimension10

Ya, I think you are right, I cleared my response.

7. May 30, 2012

### SammyS

Staff Emeritus