Решебник по алгебре 8 класс Мерзляк ФГОС Задание 201

 

\[\boxed{\text{201\ (201).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ \frac{2x + 7}{4} = \frac{x + 5}{3}\text{\ \ \ \ \ \ \ \ \ }| \cdot 12\]

\[3 \cdot (2x + 7) = 4 \cdot (x + 5)\]

\[6x + 21 = 4x + 20\]

\[6x - 4x = 20 - 21\]

\[2x = - 1\]

\[x = - \frac{1}{2}\]

\[Ответ:\ x = - 0,5.\]

\[2)\ x^{2} + 6x = 0\]

\[x(x + 6) = 0\]

\[x = 0;\ \ \ \ \ x + 6 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 6\]

\[Ответ:x = 0;\ x = - 6.\]

\[3)\ 0,21x - 0,7x^{2} = 0\]

\[0,7x(0,3 - x) = 0\]

\[0,7x = 0;\ \ \ \ \ \ \ 0,3 - x = 0\]

\[x = 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 0,3\]

\[Ответ:x = 0;x = 0,3.\]

\[4)\ x^{2} - 16 = 0\]

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

\[x - 4 = 0;\ \ \ \ \ \ x + 4 = 0\]

\[x = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 4\]

\[Ответ:x = 4;\ x = - 4.\]

\[5)\ 25x^{2} - 36 = 0\]

\[(5x - 6)(5x + 6) = 0\]

\[5x - 6 = 0;\ \ \ \ \ \ \ \ 5x + 6 = 0\]

\[5x = 6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 5x = - 6\]

\[x = \frac{6}{5} = 1,2\ \ \ \ \ \ \ \ x = - \frac{6}{5} = - 1,2\]

\[Ответ:x = 1,2;\ \ x = - 1,2.\]

\[6)\ x^{2} + 4 = 0\]

\[x^{2} = - 4\]

\[Ответ:корней\ нет.\]

\[\boxed{\text{201.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\ x + 2 = 10\ \ \ и\ \ \ 3x = 24\ \]

\[\text{\ \ \ \ \ }x = 8\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 8\]

\[уравнения\ равносильны.\]

\[2) - 2x = - 6\ \ \ \ и\ \ \frac{1}{3x} = 1\]

\[\text{\ \ \ \ \ }x = 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 3\]

\[уравнения\ равносильны.\]

\[3)\ x - 5 = 0\ \ \ \ и\ \ \ \ \ x(x - 5) = 0\]

\[x = 5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 0;\ \ x = 5\]

\[уравнения\ не\ равносильны.\]

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

\[\left\{ \begin{matrix} 3x - 12 = 0 \\ x + 2 = 0\ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = 4\ \ \ \ \\ x = - 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\]

\[и\ (0,4 - 0,1x)(7x + 14) = 0\]

\[\left\{ \begin{matrix} 0,4 - 0,1x = 0 \\ 7x + 14 = 0\ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = 4\ \ \ \\ x = - 2 \\ \end{matrix} \right.\ \]

\[уравнения\ равносильны.\]

\[5)\ \frac{6}{x} = 0\ \ \ \ \ \ \ \ и\ \ \ \ \ \ \ \ \ x^{2} = - 4\]

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

\[уравнения\ равносильны.\]

\[6)\ x + 1 = 1 + x\ \ \ \ и\ \ \ \ \ \frac{x^{2} + 1}{x^{2} + 1} = 1\]

\[x + 1 - 1 - x = 0\ \ \ \ \ \ \ \ \ 1 = 1\]

\[Решения\ уравнений - любое\ \]

\[число:\]

\[уравнения\ равносильны.\]