1. The number of real solutions $x$ that satisfy the equation
$$
\sqrt{x+5-4 \sqrt{x+1}}+\sqrt{x+10-6 \sqrt{x+1}}=1
$$
is ( ).
(A) 1
(B) 2
(C) 4
(D) infinitely many
$-1 . D$
Let $x_{0}=\sqrt{x+1}$, the equation can be rewritten as
$$
\left|x_{0}-2\right|+\left|x_{0}-3\right|=1 \text {. }
$$

Its geometric meaning is: on the number line, the sum of the distances from point $x_{0}$ to points 2 and 3 is 1.

Therefore, $x_{0}$ can take any real number satisfying $2 \leqslant x_{0} \leqslant 3$. Hence, $x=x_{0}^{2}-1$ can take infinitely many values.