Решебник по алгебре 7 класс Мерзляк ФГОС Задание 548

 

\[\boxed{\text{548\ (548).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

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

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

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

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

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

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

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

\[Ответ:x = - \frac{2}{3};4.\]

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

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

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

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

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

\[Ответ:\ x = - 7;\ - 1.\]

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

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

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

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

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

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

\[\boxed{\text{548.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\ 0,74x^{2} + 26x =\]

\[= x \cdot (0,74x + 26)\ \]

\[если\ x = 100:\]

\[100 \cdot (0,74 \cdot 100 + 26) =\]

\[= 100 \cdot (74 + 26) =\]

\[= 100 \cdot 100 = 10\ 000.\]

\[2)\ x^{2}y^{3} - x^{3}y^{2} = x^{2}y^{2} \cdot (y - x)\text{\ \ }\]

\[если\ x = 4;\ \ \ \ y = 5:\]

\[4^{2} \cdot 5^{2} \cdot (5 - 4) = 16 \cdot 25 \cdot 1 =\]

\[= 400.\ \ \]