\[\boxed{\text{219.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[\textbf{а)}\ x³ + 7x² - 6 = 0\]
\[x_{1} = - 1 \Longrightarrow корень\ уравнения\ \]
\[(методом\ подбора);\]
\[\Longrightarrow x^{3} + 7x^{2} - 6 =\]
\[= (x + 1)\left( x^{2} + 6x - 6 \right)\]
\[(x + 1)\left( x^{2} + 6x - 6 \right) = 0\]
\[x_{1} = - 1\]
\[x^{2} + 6x - 6 = 0\]
\[D = 9 + 6 = 15\]
\[x_{2,3} = - 3 \pm \sqrt{15}.\]
\[Ответ:x = - 1;x - 3 \pm \sqrt{15}.\]
\[\textbf{б)}\ x³ + 4x² - 5 = 0\]
\[x_{1} = 1 \Longrightarrow корень\ уравнения\]
\[\ (методом\ подбора);\]
\[\Longrightarrow x^{3} + 4x^{2} - 5 =\]
\[= (x - 1)\left( x^{2} + 5x + 5 \right)\]
\[(x - 1)\left( x^{2} + 5x + 5 \right) = 0\]
\[x_{1} = 1\]
\[x^{2} + 5x + 5 = 0\]
\[D = 25 - 4 \cdot 5 = 25 - 20 = 5\]
\[x_{2,3} = \frac{- 5 \pm \sqrt{5}}{2}\]
\[Ответ:x = 1;\ \ x = \frac{- 5 \pm \sqrt{5}}{2}.\]