1. The solution set of the equation $\sqrt{x^{2}+1}-\sqrt{1 x^{2}+2}=1-$ $\frac{1}{\sqrt[3]{x^{2}+1}}$ is ( ).
(A) $\{1.5,2 \sqrt{2}\}$
(B) $\left\{\frac{1}{10}, \frac{1}{\sqrt{2}}\right\}$
(C) $\left\{\frac{1}{\pi}, \sqrt{\pi}\right\}$
(D) $\varnothing$
-,1.D.
For any $x \in R, \sqrt{x^{2}+1}-\sqrt{x^{2}+2}<0$.
And $1-\frac{1}{\sqrt[3]{x^{2}+1}} \geqslant 0$, left $\neq$ right.
That is, for any $x \in R$, the equation is not satisfied, the solution set of the equation is the empty set: $\varnothing$.