ГДЗ по алгебре 7 класс Макарычев ФГОС Задание 1030

\[\boxed{\text{1030.}\text{\ }еуроки - ответы\ на\ пятёрку}\]

\[\textbf{а)}\ x³ - 2x^{2} - x + 2 = 0\]

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

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

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

\[x = 2\ \ \ \mathbf{\text{\ \ \ }}или\ \ \ x = 1\ \ \ \ \ \ или\ \ \ \]

\[\ \ x = - 1\]

\[Ответ:x = \pm 1;\ \ x = 2.\]

\[\textbf{б)}\ y³ - y^{2} = 16y - 16\]

\[y^{2}(y - 1) - 16y + 16 = 0\]

\[y^{2}(y - 1) - 16 \cdot (y - 1) = 0\]

\[(y - 1)\left( y^{2} - 16 \right) = 0\]

\[(y - 1)(y - 4)(y + 4) = 0\]

\[y = 1\ \ \ или\ \ \ \ y = 4\ \ \ \ \ или\ \ \ \ \]

\[\ y = - 4\]

\[Ответ:y = \pm 4;\ \ y = 1.\]

\[\textbf{в)}\ 2y³ - y^{2} - 32y + 16 = 0\]

\[y^{2}(2y - 1) - 16 \cdot (2y - 1) = 0\]

\[(2y - 1)(y² - 16) = 0\]

\[(2y - 1)(y - 4)(y + 4) = 0\]

\[2y = 1\ \ \ или\ \ \ \ y = 4\ \ \ \ \ \ или\]

\[\ \ \ \ \ y = - 4\]

\[y = 0,5\]

\[Ответ:y = 0,5;\ \ y = \pm 4.\]

\[\textbf{г)}\ \ 4x³ - 3x^{2} = 4x - 3\]

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

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

\[(4x - 3)(x - 1)(x + 1) = 0\]

\[4x = 3\ \ \ \ или\ \ \ \ x = 1\ \ \ \ или\ \]

\[\ \ x = - 1\]

\[x = \frac{3}{4}\]

\[Ответ:x = \pm 1;\ \ x = \frac{3}{4}.\]