Solve the following equation:

$$
\sqrt{x+2 \sqrt{x-1}}+\sqrt{x-2 \sqrt{x-1}}=2
$$
The expressions under the square root are equal to $(\sqrt{x-1} \pm 1)^{2}$. Then, using the identity $\sqrt{a^{2}}=|a|$, the equation can be solved. Every solution $x$ that satisfies $1 \leqq x \leqq 2$.