Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 599

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\[1)\ x^{3} - 3x^{2} + 2x - 6 > 2x^{3} -\]

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

\[x^{3} + 2x^{2} + 2x + 4 < 0\]

\[x^{2}(x + 2) + 2(x + 2) < 0\]

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

\[x + 2 < 0\]

\[x < - 2.\]

\[2)\ x^{3} - 3x^{2} - 4x + 12 > - 3x^{3} +\]

\[+ x^{2} + 12x - 4\]

\[4x^{3} - 4x^{2} - 16x + 16 > 0\]

\[4x^{2}(x - 1) - 16(x - 1) > 0\]

\[\left( 4x^{2} - 16 \right)(x - 1) > 0\]

\[(2x - 4)(2x + 4)(x - 1) > 0\]

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

\[- 2 < x < 1\ \ и\ \ x > 2.\]