Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 1568

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\[2x^{3} + mx^{2} + nx + 12 = 0\]

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

\[4( - 14 - n) - 2n - 4 = 0\]

\[- 56 - 4n - 2n - 4 = 0\]

\[- 6n - 60 = 0\]

\[n + 10 = 0\]

\[n = - 10;\]

\[m = - 14 + 10 = - 4.\]

\[Третий\ корень:\]

\[2x^{3} - 4x^{2} - 10x + 12 = 0\]

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

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

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

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

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

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

\[(x + 2)(x - 1)(x - 3) = 0\]

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

\[Ответ:\ \ x_{3} = 3.\]