Solve for x : x + 1/x = 3
Question
Solve for x:
\[ x+\frac{1}{x}=3, \qquad x\ne0 \]Solution
Multiplying both sides by \(x\),
\[ x^2+1=3x \]
\[ x^2-3x+1=0 \]
Using the quadratic formula,
\[ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \]
\[ x=\frac{3\pm\sqrt{9-4}}{2} \]
\[ x=\frac{3\pm\sqrt5}{2} \]
Answer
\[
\boxed{x=\frac{3+\sqrt5}{2}\quad \text{or}\quad x=\frac{3-\sqrt5}{2}}
\]