Example 2. Solve the equation $\sqrt{x^{2}-x-2}+\sqrt{x^{2}-3 x+5}$ $=3$.

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Solve the equation $\left(x^{2}-x-2\right)-\left(x^{2}-3 x+5\right)$ $=2 x-7$ by dividing both sides by the original equation, then adding it to the original equation, and squaring to organize:
$$
8 x^{2}-11 x-19=0 \text {. }
$$

Solving yields: $x_{1}=-1, x_{2}=2 \frac{3}{8}$ (extraneous root). (Author's affiliation: Yizhang Normal School, Hunan)