Алгебра
Английский
Биология
География
Геометрия
История
Русский
Обществознание
Физика
Химия
Информатика
Литература
МатематикаРешебник по алгебре 8 класс Мерзляк ФГОС Задание 596
Задание 596
\[\boxed{\mathbf{596\ (596).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ \sqrt{x} = x\]
\[y = \sqrt{x},\ \ y = x\]
| \[x\] | \[1\] | \[4\] | \[9\] |
|---|---|---|---|
| \[y\] | \[1\] | \[2\] | \[3\] |
\[Ответ:x = 1;x = 0.\]
\[2)\ \sqrt{x} = x²\]
\[y = \sqrt{x},\ \ y = x^{2}\]
| \[x\] | \[1\] | \[2\] | \[3\] |
|---|---|---|---|
| \[y\] | \[1\] | \[4\] | \[9\] |
\[Ответ:x = 1;x = 0.\]
\[3)\ \sqrt{x} = x + 2\]
\[y = \sqrt{x},\ \ y = x + 2\]
| \[x\] | \[1\] | \[2\] | \[- 1\] |
|---|---|---|---|
| \[y\] | \[3\] | \[4\] | \[1\] |
\[Ответ:нет\ корней.\]
\[4)\sqrt{x} = 0,5x + 0,5\]
\[y = \sqrt{x},\ \ y = 0,5x + 0,5\]
| \[x\] | \[1\] | \[2\] | \[- 1\] |
|---|---|---|---|
| \[y\] | \[1\] | \[1,5\] | \[0\] |
\[Ответ:x = 1.\]
\[5)\ \sqrt{x} = \frac{8}{x}\]
\[y = \sqrt{x},\ \ y = \frac{8}{x}\]
| \[x\] | \[2\] | \[4\] | \[- 2\] | \[- 4\] |
|---|---|---|---|---|
| \[y\] | \[4\] | \[2\] | \[- 4\] | \[- 2\] |
\[Ответ:x = 4.\]
\[6)\ \sqrt{x} = 1,5 - 0,5x\]
\[y = \sqrt{x},\ \ y = 1,5 - 0,5x\]
| \[x\] | \[1\] | \[2\] |
|---|---|---|
| \[y\] | \[1\] | \[0,5\] |
\[Ответ:x = 1.\]
\[\boxed{\mathbf{5}\mathbf{9}\mathbf{6}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ \frac{\left( \sqrt{b} - \sqrt{a} \right)^{2}}{(a - b)\left( \sqrt{a} + \sqrt{b} \right)} =\]
\[= \frac{\left( \sqrt{b} - \sqrt{a} \right)^{2}}{\left( \sqrt{a} - \sqrt{b} \right)\left( \sqrt{a} + \sqrt{b} \right)^{2}} =\]
\[= \frac{- \sqrt{b} + \sqrt{a}}{\left( \sqrt{a} + \sqrt{b} \right)^{2}}\]
\[2)\frac{\sqrt{a} - \sqrt{b}}{a + \sqrt{\text{ab}}} - \frac{\sqrt{a} - \sqrt{b}}{\left( \sqrt{a} + \sqrt{b} \right)^{2}} =\]
\[= \frac{a - b - a + \sqrt{\text{ab}}}{\sqrt{a} \cdot \left( \sqrt{a} + \sqrt{b} \right)^{2}} =\]
\[= \frac{\sqrt{\text{ab}} - b}{\sqrt{a} \cdot \left( \sqrt{a} + \sqrt{b} \right)^{2}}\ \]
\[3)\ \frac{\sqrt{\text{ab}} - b}{\sqrt{a} \cdot \left( \sqrt{a} + \sqrt{b} \right)^{2}}\ :\frac{\sqrt{a} - \sqrt{b}}{a + \sqrt{\text{ab}}} =\]
\[= \frac{\sqrt{b}}{\sqrt{a} + \sqrt{b}}\]
\[1)\ \sqrt{a} + \sqrt{b} - \frac{2\sqrt{\text{ab}}}{\sqrt{a} + \sqrt{b}} =\]
\[= \frac{a + \sqrt{\text{ab}} + \sqrt{\text{ab}} + b - 2\sqrt{\text{ab}}}{\sqrt{a} + \sqrt{b}} =\]
\[= \frac{a + b}{\sqrt{a} + \sqrt{b}}\]
\[2)\ \frac{\sqrt{a} - \sqrt{b}}{\sqrt{a} + \sqrt{b}} + \frac{\sqrt{b}}{\sqrt{a}} =\]
\[= \frac{a - \sqrt{\text{ab}} + \sqrt{\text{ab}} + b}{\sqrt{a} \cdot \left( \sqrt{a} + \sqrt{b} \right)} =\]
\[= \frac{a + b}{\sqrt{a} \cdot \left( \sqrt{a} + \sqrt{b} \right)}\]
\[3)\frac{(a + b) \cdot \sqrt{a} \cdot (\sqrt{a} + \sqrt{b})}{(\sqrt{a} + \sqrt{b})(a + b)} = \sqrt{a}\ \]
