# 11.2 Solve the equation

$$
\frac{1}{\sqrt{x+20}+\sqrt{x+21}}+\frac{1}{\sqrt{x+21}+\sqrt{x+22}}=1
$$
Solution 1: By multiplying both fractions by their conjugates, we get $\sqrt{x+22}-\sqrt{x+20}=1$. Multiplying this by its conjugate and transforming, we get $\sqrt{x+22}+\sqrt{x+20}=2$. Adding the two equations, we get $\sqrt{x+22}=\frac{3}{2}, x=-\frac{79}{4}$. Substituting this number into the original equation, we verify that everything checks out.

Solution 2: The left side monotonically decreases, so the equation has no more than one root. By substitution, we confirm that $x=-\frac{79}{4}$ works.

Criteria: Inequivalent transformations without justification or subsequent verification - 2 points are deducted.