\[x^{2} - 5x + 2 = 0\]
\[x_{1}^{2} + 4x_{1}x_{2} + x_{2}^{2} =\]
\[= \left( x_{1} + x_{2} \right)^{2} + 2x_{1}x_{2} =\]
\[= 5^{2} + 2 \cdot 2 = 25 + 4 = 29.\]