Решебник по алгебре 7 класс Мерзляк ФГОС Задание 670

 

\[\boxed{\text{670\ (670).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[НОК\ (1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7) =\]

\[= 2 \cdot 3 \cdot 2 \cdot 5 \cdot 7 = 420\]

\[1 = 1,\ \ 2 = 2 \cdot 1,\ \ \]

\[3 = 3 \cdot 1,\ \ 4 = 2 \cdot 2\]

\[5 = 5 \cdot 1,\ \ 6 = 2 \cdot 3,\]

\[\ \ 7 = 7 \cdot 1\]

\[Ответ:420\ дней.\]

\[\boxed{\text{670.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\ (3x - 5)^{2} - 49 = 0\]

\[(3x - 5)^{2} - 7^{2} = 0\]

\[(3x - 5 - 7)(3x - 5 + 7) = 0\]

\[(3x - 12)(3x + 2) = 0\]

\[3x - 12 = 0;\ \ \ \ \ \ 3x + 2 = 0\]

\[3x = 12\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3x = - 2\]

\[x = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - \frac{2}{3}\]

\[Ответ:x = - \frac{2}{3};4.\]

\[2)\ (4x + 7)^{2} - 9x^{2} = 0\]

\[(4x + 7 - 3x)(4x + 7 + 3x) = 0\]

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

\[x + 7 = 0,\ \ 7x + 7 = 0\]

\[x = - 7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 1\]

\[Ответ:\ x = - 7;\ - 1.\]

\[3)\ (a - 1)^{2} - (2a + 9)^{2} = 0\]

\[( - a - 10)(3a + 8) = 0\]

\[- a - 10 = 0,\ \ 3a + 8 = 0\]

\[Ответ:\ x = - 10;\ - 2\frac{2}{3}.\]

\[(7b + 9)(23b + 1) = 0\]

\[Ответ:\ x = - 1\frac{2}{7};\ - \frac{1}{23}.\]