ГДЗ по алгебре 8 класс Макарычев Задание 537

\[\boxed{\text{537\ (537).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[\textbf{а)}\ x^{2} - 11x + 31 = 1\]

\[x^{2} - 11x + 30 = 0\]

\[D = 121 - 120 = 1\]

\[x_{1,2} = \frac{11 \pm \sqrt{1}}{2} = \frac{11 \pm 1}{2}\]

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

\[Ответ:при\ x = 5;\ \ x = 6.\]

\[\textbf{б)}\ x^{2} - 5x - 3 = 2x - 5\]

\[x^{2} - 7x + 2 = 0\]

\[D = 49 - 8 = 41\]

\[x_{1,2} = \frac{7 \pm \sqrt{41}}{2}\]

\[x_{1} = \frac{7 - \sqrt{41}}{2};\ \ x_{2} = \frac{7 + \sqrt{41}}{2}\]

\[Ответ:при\ x = \frac{7 \pm \sqrt{41}}{2}.\]

\[\textbf{в)}\ 7x + 1 = 3x^{2} - 2x + 1\]

\[3x^{2} - 9x = 0\]

\[3x(x - 3) = 0\]

\[x_{1} = 0,\ \ \ \ x_{2} = 3\ \]

\[Ответ:при\ x = 0;\ \ x = 3.\]

\[\textbf{г)} - 2x^{2} + 5x + 6 = 4x^{2} + 5x\]

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

\[6 \cdot \left( x^{2} - 1 \right) = 0\]

\[x^{2} - 1 = 0\]

\[x^{2} = 1\]

\[x_{1,2} = \pm 1\ \ \]

\[Ответ:при\ x = \pm 1.\]