I need help solving a competition math problem.

Question

I was doing a practice test for a math competition, and I came across a problem I am unable to solve, and I have tried to get help, with no luck. I need to be able to solve it without a calculator too. The problem is: "If $x^2+1/x^2=3$ and $x > 0$, what is the value of $x+1/x$. Express your answer in simplest radical form." I tried manipulating the first equation and I end up with $x^4-3x^2+1=0$, and there is no way I can figure out how to factor it. I would appreciate any help I can get with this problem!

Answer 1

Notice that $x^2 \frac{1}{x^2} = 1$. We could add 2 to both sides of the equation to complete the square. $$ (x + \frac{1}{x})^2 = 5$$

Answer 2

Guide:

Let $y=x^2$, solve for $y$ using the quadratic formula.

After you get your $y$, you can solve for the corresponding $x$.