Решебник по алгебре 7 класс Мерзляк ФГОС Задание 621

 

\[\boxed{\text{621\ (621).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ (x - 1)^{2} + (x + 1)^{2} = - 10\ \ \]

\[(x - 1)^{2} \geq 0;\ \ \ \ \ \ \ \ (x + 1) \geq 0\]

\[Следовательно,\ таких\ \]

\[значений\ \text{x\ }не\ существует.\]

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

\[(x - 1)^{2} \geq 0 \Longrightarrow \ \ x - 1 = 0 \Longrightarrow\]

\[\Longrightarrow \ \ x = 1\]

\[(x + 1)^{2} \geq 0 \Longrightarrow \ \ x + 1 = 0 \Longrightarrow \ \]

\[\Longrightarrow \ x = - 1\]

\[Следовательно,\ нет\ таких\ \]

\[значений\ x.\]

\[(x + 1)^{2} \geq 0 \Longrightarrow \ \ x + 1 = 0 \Longrightarrow\]

\[\Longrightarrow \ \ x = - 1\]

\[Ответ:\ \ при\ \ x = - 1.\]

\[\boxed{\text{621.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

Пояснение.

Решение.

\[1)\ \left( a^{2} - 3 \right)\left( a^{2} + 3 \right) =\]

\[= \left( a^{2} \right)^{2} - 3^{2} = a^{4} - 9\]

\[2)\ \left( 5 + b^{2} \right)\left( b^{2} - 5 \right) =\]

\[= \left( b^{2} \right)^{2} - 5^{2} = b^{4} - 25\]

\[3)\ \left( 3x - 2y^{2} \right)\left( 3x + 2y^{2} \right) =\]

\[= (3x)^{2} - \left( 2y^{2} \right)^{2} = 9x^{2} - 4y^{4}\]

\[4)\ \left( 10p^{3} - 7k \right)\left( 10p^{3} + 7k \right) =\]

\[= \left( 10p^{3} \right)^{2} - (7k)^{2} =\]

\[= 100p^{6} - 49k^{2}\]

\[5)\ \left( 4x^{2} - 8y^{3} \right)\left( 4x^{2} + 8y^{3} \right) =\]

\[= \left( 4x^{2} \right)^{2} - \left( 8y^{3} \right)^{2} =\]

\[= 16x^{4} - 64y^{6}\]

\[6)\ \left( 11a^{3} + 5b^{2} \right)\left( 5b^{2} - 11a^{3} \right) =\]

\[= \left( 5b^{2} \right)^{2} - \left( 11a^{3} \right)^{2} =\]

\[= 25b^{4} - 121a^{6}\]

\[7)\ (7 - xy)(7 + xy) =\]

\[= 7^{2} - \left( \text{xy} \right)^{2} = 49 - x^{2}y^{2}\]

\[= \left( 8a^{3}b \right)^{2} - \left( \frac{1}{3}ab^{2} \right)^{2} =\]

\[= 64a^{6}b^{2} - \frac{1}{9}a^{2}b^{4}\]

\[= \left( 0,3m^{5} \right)^{2} - \left( 0,1n^{3} \right)^{2} =\]

\[= 0,09m^{10} - 0,01n^{6}\]

\[= \left( \frac{7}{9}a^{2}c \right)^{2} - \left( 1,4b^{4} \right)^{2} =\]

\[- \frac{49}{81}a^{4}c^{2} - 1,96b^{8}\]