Решебник по алгебре 9 класс Мерзляк Задание 92

\[\boxed{\text{92\ (92).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1.\]

\[1)\ 4x + 6 = 2x - 3\]

\[4x - 2x = - 3 - 6\]

\[2x = - 9\]

\[x = - 4,5.\]

\[2)\ 4x + 3 = 2x - 6\]

\[4x - 2x = - 6 - 3\]

\[2x = - 4,5.\]

\[Равносильны.\]

\[2.\]

\[1)\ 8x - 4 = 0\ \]

\[8x = 4\]

\[x = 0,5.\]

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

\[2x = 1\]

\[x = 0,5.\]

\[Равносильны.\]

\[3.\]

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

\[= 3 - x\]

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

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

\[Равносильны.\]

\[4)\ \frac{x^{2} - 1}{x + 1} = 0\ \ и\ \text{\ x}^{2} - 1 = 0\]

\(x^{2} = 1\)

\(x^{2} = \pm 1\)

\[x \neq - 1\]

\[x = 1.\]

\[x^{2} = 1\]

\[x = 1\]

\[x = - 1.\]

\[Неравносильны.\]

\[5)\ \frac{x^{2} - 1}{x + 1} = 0\ \ \ и\ \ x - 1 = 0\]

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

\[x \neq - 1\]

\[x = 1.\]

\[Равносильны.\]

\[6)\ x^{2} + 1 = 0\ \ \ и\ \ 0 \cdot x = 5\]

\[нет\ корней\ \ \ \ \ \ \ \ нет\ корней.\]

\[Равносильны.\]