Решебник по алгебре 11 класс Никольский Параграф 7. Равносильность уравнений и неравенств Задание 22

\[\boxed{\mathbf{22.}}\]

\[\textbf{а)}\ \sqrt[3]{3x^{3} - 3x^{2} - x + 5} >\]

\[> \sqrt[3]{2x^{3} - 4x^{2} + x + 5}\]

\[3x^{3} - 3x^{2} - x + 5 > 2x^{3} -\]

\[- 4x^{2} + x + 5\]

\[x^{3} + x^{2} - 2x > 0\]

\[x\left( x^{2} + x - 2 \right) > 0\]

\[x^{2} + x - 2 = (x + 2)(x - 1)\]

\[x_{1} + x_{2} = - 1;\ \ x_{1} \cdot x_{2} = - 2\]

\[x_{1} = - 2;\ \ x_{2} = 1.\]

\[(x + 2)x(x - 1) > 0\]

\[- 2 < x < 0;\]

\[x > 1.\]

\[x^{3} - 5x^{2} + 6x < 0\]

\[x\left( x^{2} - 5x + 6 \right) < 0\]

\[x^{2} - 5x + 6 = (x - 2)(x - 3)\]

\[x_{1} + x_{2} = 5;\ \ x_{1} \cdot x_{2} = 6\]

\[x_{1} = 2;\ \ x_{2} = 3.\]

\[x(x - 2)(x - 3) < 0\]

\[x < 0;\]

\[2 < x < 3.\]