Math Problem Solver

$$x + \frac{1}{x} = \frac{1}{2 \sqrt{2} + 3} + 2 \sqrt{2} + 3$$

The solution is: $$x = 3 + 2 \sqrt{2} \approx 5.8284271$$

By substituting this value into the expression, we find that: $$\begin{aligned}x + \frac{1}{x} &= \frac{1}{2 \sqrt{2} + 3} + \left(2 \sqrt{2} + 3\right)\\&= \frac{1}{2 \sqrt{2} + 3} + 2 \sqrt{2} + 3\end{aligned}$$