\[\boxed{\text{1273.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[x^{4} - 5x^{3} - 4x^{2} - 7x + 4 = 0\]
\[\left( x^{4} - 4x^{2} + 4 \right) - 5x^{3} - 7x = 0\]
\[\left( x^{2} - 2 \right)^{2} - 5x^{3} - 7x = 0\]
\[\left\{ \begin{matrix} \left( x^{2} - 2 \right)^{2} \geq 0 \\ 5x^{2} + 7 > 0\ \ \\ \end{matrix} \right.\ \Longrightarrow x \geq 0,\]
\[\text{\ \ }ч.т.д.\]