3. The real numbers $x_{1}, x_{2}$, and $x_{3}$ are the three roots of the equation $2 x^{3}-(p-4) x^{2}-(2 p-1) x-p+8=0$, considering their possible multiplicities. Find the smallest value of the expression $x_{1}^{2}+x_{2}^{2}+x_{3}^{2}$ under these conditions. For which $p$ is it realized?
Answer: the minimum value $\frac{417}{64}$ is achieved at $p=\frac{15}{4}$.