Решебник по алгебре 7 класс Мерзляк ФГОС Задание 660

 

\[\boxed{\text{660\ (660).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[a^{2} + b^{2} = 34;\ \ ab = 15;\ \ \]

\[a > 0;\ \ b > 0\]

\[(a + b)^{2} = a^{2} + 2\text{ab} + b^{2} =\]

\[= 34 + 2 \cdot 15 = 34 + 30 = 64\]

\[тогда\ a + b = 8.\]

\[Ответ:8.\]

\[\boxed{\text{660.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\ x^{2} - 49 = 0\]

\[(x - 7)(x + 7) = 0\]

\[x - 7 = 0;\ \ \ x + 7 = 0\]

\[x = 7;\ \ \ \ \ \ \ \ \ \ \ x = - 7\]

\[Ответ:\ x = \pm 7.\]

\[2)\ \frac{1}{4} - z^{2} = 0\]

\[\left( \frac{1}{2} - z \right)\left( \frac{1}{2} + z \right) = 0\]

\[\frac{1}{2} - z = 0;\ \ \ \ \frac{1}{2} + z = 0\]

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

\[Ответ:\ x = \pm \frac{1}{2}\text{.\ }\]

\[3)\ x^{2} + 36 = 0\]

\[x^{2} = - 36\]

\[Ответ:нет\ корней.\]

\[4)\ x^{2} - 0,01 = 0\]

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

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

\[x = 0,1\ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 00,1\]

\[Ответ:\ x = \pm 0,1.\]

\[5)\ 9x^{2} - 4 = 0\]

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

\[3x - 2 = 0;\ \ \ \ \ \ 3x + 2 = 0\]

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

\[x = \frac{2}{3}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - \frac{2}{3}\]

\[Ответ:\ x = \pm \frac{2}{3}.\]

\[6)\ 0,04x^{2} - 1 = 0\]

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

\[0,2x - 1 = 0;\ \ \ \ 0,2x + 1 = 0\]

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

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

\[Ответ:\ x = \pm 5.\]