Example 2. If the three equations $\mathrm{x}^{2}+4 \mathrm{ax}-4 \mathrm{a}+3=0$, $x^{2}+(a-1) x+a^{2}=0, x^{2}+2 a x-2 a=0$, have at least one real solution, try to find the range of the real number $\mathrm{a}$.

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Solve $\left\{\begin{array}{l}(4 a)^{2}-4(-4 a+3)<0, \\ (a-1)^{2}-4 a^{2}<0, \\ 4 a^{2}-4(-2 a)<0 .\end{array}\right.$
to get $-\frac{3}{2}<\mathrm{a}<-1$. When $\mathrm{a}$ satisfies the above inequality,
all three equations have no real solutions, so when at least one of the three equations has a real solution, the range of $\mathrm{a}$ is ( $-\infty$,
$$
\left.-\frac{3}{2}\right] \cup[-1,+\infty) \text {. }
$$