x is a real number such that x - 1/x = 3. Find all possible values of x + 1/x.
+781 \(x-1/x=3\\ x^2-1=3x\\ x^2-3x-1=0\\ x=\frac{3\pm\sqrt{13}}{2}\\ \)
So
x+1/x
=\(\frac{3+\sqrt{13}}{2}+\frac{1}{3+\frac{\sqrt{13}}{{2}}}\\ =\sqrt{13}\)
x+1\x
\(\frac{3-\sqrt{13}}{2}+\frac{1}{3-\frac{\sqrt{13}}{{2}}}\\ =-\sqrt{13}\)
So I believe the possible values of x+1/x are \(\boxed{\sqrt{13}\ \text{and}\ -\sqrt{13}.}\)
