Решебник по алгебре 8 класс Мерзляк ФГОС Задание 165

\[\boxed{\text{165\ (165).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[x^{2} + \frac{1}{x^{2}} = 6;\ \ \ \ x - \frac{1}{x} = ?\]

\[\left( x - \frac{1}{x} \right)^{2} = x^{2} - 2 + \frac{1}{x^{2}} =\]

\[= 6 - 2 = 4\]

\[\left( x - \frac{1}{x} \right)^{2} = 4\]

\[\left\{ \begin{matrix} x - \frac{1}{x} = 2\ \ \ \\ x - \frac{1}{x} = - 2 \\ \end{matrix} \right.\ \]

\[Ответ:2;\ \ - 2.\]

\[\boxed{\text{165.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\frac{25 - 5a + 5b - ab}{25 + 5a - 5b - ab} \cdot\]

\[\cdot \frac{ab - 5a - 5b + 25}{ab + 5a + 5b + 25} =\]

\[= \frac{\left( 5(5 - a) + b(5 - a) \right)\left( a(b - 5) - 5(b - 5) \right)}{\left( 5(5 + a) - b(5 + a) \right)\left( a(b + 5) + 5(b + 5) \right)} =\]

\[= \frac{(5 - a)(5 + b)(b - 5)(a - 5)}{(5 + a)(5 - b)(b + 5)(a + 5)} =\]

\[= \frac{(a - 5)^{2}}{(a + 5)^{2}}\]

\[2)\ \frac{a^{2} - 2ab + b^{2}}{a^{2} - ab - 4a + 4b}\ :\]

\[:\frac{a^{2} - ab + 4a - 4b}{a^{2} - 16} =\]

\[= \frac{(a - b)^{2}(a - 4)(a + 4)}{(a - b)(a - 4)(a - b)(a + 4)} =\]

\[= 1\]