1. Let $x_{1}, x_{2}$ be the real roots of the equation
$$
2 x^{2}-4 m x+2 m^{2}+3 m-2=0
$$

When $m$ is what value, $x_{1}^{2}+x_{2}^{2}$ has the minimum value? And find this minimum value.
(2001, Jiangsu Province Junior High School Mathematics Competition)
Answer: When $m=\frac{2}{3}$, $x_{1}^{2}+x_{2}^{2}$ attains its minimum value $\frac{8}{9}$. )