Answer
$\sum x=5$
Work Step by Step
Given that $x_1=3$ is a solution, we divide the polynomial $f(x)=x^3-8x^2+16x-3$ by $x-3$:
$\begin{array}{lllll}
\underline{3}| & 1&-8 & 16 &-3 \\
& & 3 & -15& 3\\
& -- & -- & -- & --\\
& 1 & -5 & 1& |\underline{0}
\end{array}$
We can write:
$f(x)=(x-3)(x^{2} -5x+1)$
The solutions $x_2$ and $x_3$ are the zeros of the trinomial $x^2-5x+1$, therefore we have:
$x_2+x_3=-\frac{-5}{1}=5$
