Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 1562

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

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

\[x^{2}(x - 3) + (x - 3) = 0\]

\[\left( x^{2} + 1 \right)(x - 3) = 0\]

\[\left( x^{2} + 1 \right)(x - 3) = 0\]

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

\[2)\ x^{3} - 3x^{2} - 4x + 12 = 0\]

\[x^{2}(x - 3) - 4(x - 3) = 0\]

\[\left( x^{2} - 4 \right)(x - 3) = 0\]

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

\[3)\ x^{4} - 3x^{3} - 2x^{2} - 6x - 8 = 0\]

\[\left( x^{4} - 4x^{3} + 2x^{2} - 8x \right) + \left( x^{3} - 4x^{2} + 2x - 8 \right) = 0\]

\[(x + 1)\left( x^{3} - 4x^{2} + 2x - 8 \right) = 0\]

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

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

\[x_{1} = - 1;\ x_{2,3} = \pm i\sqrt{2};\ \ x_{4} = 4.\]