| Предыдущая версия справа и слеваПредыдущая версияСледующая версия | Предыдущая версияСледующая версияСледующая версия справа и слева |
| math-public:up_s_b_bez_otvetov [2020/01/16 19:24] – labreslav | math-public:up_s_b_bez_otvetov [2020/01/17 11:10] – labreslav |
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| | \\ 16. | \\ $\left(\dfrac{\sqrt{a}-\sqrt{b}}{a\sqrt{b}+b\sqrt{a}}+\dfrac{\sqrt{a}+\sqrt{b}}{a\sqrt{b}-b\sqrt{a}}\right)\cdot\dfrac{\left(\sqrt{a}\right)^3\cdot\sqrt{b}}{a+b}-\dfrac{2b}{a-b}$\\ | | | \\ 16. | \\ $\left(\dfrac{\sqrt{a}-\sqrt{b}}{a\sqrt{b}+b\sqrt{a}}+\dfrac{\sqrt{a}+\sqrt{b}}{a\sqrt{b}-b\sqrt{a}}\right)\cdot\dfrac{\left(\sqrt{a}\right)^3\cdot\sqrt{b}}{a+b}-\dfrac{2b}{a-b}$\\ | |
| | \\ 17. | \\ $\sqrt{\dfrac{x}{x-a^2}}:\left(\dfrac{\sqrt{x}-\sqrt{x-a^2}}{\sqrt{x}+\sqrt{x-a^2}}-\dfrac{\sqrt{x}+\sqrt{x-a^2}}{\sqrt{x}-\sqrt{x-a^2}}\right)$\\ | | | \\ 17. | \\ $\sqrt{\dfrac{x}{x-a^2}}:\left(\dfrac{\sqrt{x}-\sqrt{x-a^2}}{\sqrt{x}+\sqrt{x-a^2}}-\dfrac{\sqrt{x}+\sqrt{x-a^2}}{\sqrt{x}-\sqrt{x-a^2}}\right)$\\ | |
| | \\ 18. | \\ $\left(\dfrac{1}{\sqrt{a}-\sqrt{a-b}}+\dfrac{1}{\sqrt{a}+\sqrt{a-b}}\right):\left(1+\sqrt{\dfrac{a+b}{a-b}}\right)$\\ | | | \\ 18. | \\ $\left(\dfrac{1}{\sqrt{a}+\sqrt{a+b}}+\dfrac{1}{\sqrt{a}-\sqrt{a-b}}\right):\left(1+\sqrt{\dfrac{a+b}{a-b}}\right)$\\ | |
| | \\ 19. | \\ $\dfrac{a\left(\dfrac{\sqrt{a}+\sqrt{b}}{2b\sqrt{a}}\right)^{-1}+b\left(\dfrac{\sqrt{a}+\sqrt{b}}{2a\sqrt{b}}\right)^{-1}}{\left(\dfrac{a+\sqrt{ab}}{2ab}\right)^{-1}+\left(\dfrac{b+\sqrt{ab}}{2ab}\right)^{-1}}$\\ | | | \\ 19. | \\ $\dfrac{a\left(\dfrac{\sqrt{a}+\sqrt{b}}{2b\sqrt{a}}\right)^{-1}+b\left(\dfrac{\sqrt{a}+\sqrt{b}}{2a\sqrt{b}}\right)^{-1}}{\left(\dfrac{a+\sqrt{ab}}{2ab}\right)^{-1}+\left(\dfrac{b+\sqrt{ab}}{2ab}\right)^{-1}}$\\ | |
| | \\ 20. | \\ $\left(\dfrac{\sqrt{a}+\sqrt{x}}{\sqrt{a+x}}-\dfrac{\sqrt{a+x}}{\sqrt{a}+\sqrt{x}}\right)^{-2}-\left(\dfrac{\sqrt{a}-\sqrt{x}}{\sqrt{a+x}}-\dfrac{\sqrt{a+x}}{\sqrt{a}-\sqrt{x}}\right)^{-2}$\\ | | | \\ 20. | \\ $\left(\dfrac{\sqrt{a}+\sqrt{x}}{\sqrt{a+x}}-\dfrac{\sqrt{a+x}}{\sqrt{a}+\sqrt{x}}\right)^{-2}-\left(\dfrac{\sqrt{a}-\sqrt{x}}{\sqrt{a+x}}-\dfrac{\sqrt{a+x}}{\sqrt{a}-\sqrt{x}}\right)^{-2}$\\ | |
| | \\ 56. (2.090 Сканави) | \\ $\dfrac{\dfrac{(a-b)^3}{(\sqrt{a}+\sqrt{b})^3}+2a\sqrt{a}+b\sqrt{b}}{a\sqrt{a}+b\sqrt{b}}+\dfrac{3(\sqrt{ab}-b)}{a-b} $\\ | | | \\ 56. (2.090 Сканави) | \\ $\dfrac{\dfrac{(a-b)^3}{(\sqrt{a}+\sqrt{b})^3}+2a\sqrt{a}+b\sqrt{b}}{a\sqrt{a}+b\sqrt{b}}+\dfrac{3(\sqrt{ab}-b)}{a-b} $\\ | |
| | \\ 57. (2.093 Сканави) | \\ $\left(\dfrac{\sqrt{3}+1}{1+\sqrt{3}+\sqrt{t}}+\dfrac{\sqrt{3}-1}{1-\sqrt{3}+\sqrt{t}}\right)\left(\sqrt{t}-\dfrac{2}{\sqrt{t}}+2\right) $\\ | | | \\ 57. (2.093 Сканави) | \\ $\left(\dfrac{\sqrt{3}+1}{1+\sqrt{3}+\sqrt{t}}+\dfrac{\sqrt{3}-1}{1-\sqrt{3}+\sqrt{t}}\right)\left(\sqrt{t}-\dfrac{2}{\sqrt{t}}+2\right) $\\ | |
| | \\ 58. (2.096 Сканави) | \\ $\sqrt{\dfrac{x}{(x-a)^2}}:\left(\dfrac{\sqrt{x}-\sqrt{x-a^2}}{\sqrt{x}+\sqrt{x-a^2}}-\dfrac{\sqrt{x}+\sqrt{x-a^2}}{\sqrt{x}-\sqrt{x-a^2}}\right) $\\ | | | \\ 58. (2.096 Сканави) | \\ $\sqrt{\dfrac{x}{x-a^2}}:\left(\dfrac{\sqrt{x}-\sqrt{x-a^2}}{\sqrt{x}+\sqrt{x-a^2}}-\dfrac{\sqrt{x}+\sqrt{x-a^2}}{\sqrt{x}-\sqrt{x-a^2}}\right) $\\ | |
| | \\ 59. (2.097 Сканави) | \\ $\dfrac{\left(\sqrt{x}+2\right)\left(\dfrac{2}{\sqrt{x}-1}-\sqrt{x}-2\right)\left(\dfrac{2}{\sqrt{x}+1}-\dfrac{8}{\sqrt{x}}\right)}{\left(2-\sqrt{x+2}\right):\left(\sqrt{\dfrac{2}{x}+1}-\dfrac{2}{\sqrt{x}}\right)} $\\ | | | \\ 59. (2.097 Сканави) | \\ $\dfrac{\left(\sqrt{x}+2\right)\left(\dfrac{2}{\sqrt{x}-1}-\sqrt{x}-2\right)\left(\dfrac{2}{\sqrt{x}+1}-\dfrac{8}{\sqrt{x}}\right)}{\left(2-\sqrt{x+2}\right):\left(\sqrt{\dfrac{2}{x}+1}-\dfrac{2}{\sqrt{x}}\right)} $\\ | |
| | \\ 60. (2.100 Сканави) | \\ $\dfrac{(z-z\sqrt{z}+2-2\sqrt{z})^2(1+\sqrt{z})^2}{z-2+\dfrac{1}{z}}-z\sqrt{z}\cdot\sqrt{\dfrac{4}{z}+4+z} $\\ | | | \\ 60. (2.100 Сканави) | \\ $\dfrac{(z-z\sqrt{z}+2-2\sqrt{z})^2(1+\sqrt{z})^2}{z-2+\dfrac{1}{z}}-z\sqrt{z}\cdot\sqrt{\dfrac{4}{z}+4+z} $\\ | |
| | \\ 67. (2.143 Сканави) | \\ $\dfrac{2b\sqrt{x^2-1}}{x-\sqrt{x^2-1}}$ , при $ x=\dfrac{1}{2}\left(\sqrt{\dfrac{a}{b}}+\sqrt{\dfrac{b}{a}}\right);a>0,b>0 $\\ | | | \\ 67. (2.143 Сканави) | \\ $\dfrac{2b\sqrt{x^2-1}}{x-\sqrt{x^2-1}}$ , при $ x=\dfrac{1}{2}\left(\sqrt{\dfrac{a}{b}}+\sqrt{\dfrac{b}{a}}\right);a>0,b>0 $\\ | |
| | \\ 68. (2.144 Сканави) | \\ $\dfrac{2a\sqrt{1+x^2}}{x+\sqrt{1+x^2}}$ , при $ x=\dfrac{1}{2}\left(\sqrt{\dfrac{a}{b}}-\sqrt{\dfrac{b}{a}}\right);a>0,b>0 $\\ | | | \\ 68. (2.144 Сканави) | \\ $\dfrac{2a\sqrt{1+x^2}}{x+\sqrt{1+x^2}}$ , при $ x=\dfrac{1}{2}\left(\sqrt{\dfrac{a}{b}}-\sqrt{\dfrac{b}{a}}\right);a>0,b>0 $\\ | |
| | \\ 69. (2.145 Сканави) | \\ $\dfrac{1-ax}{1+ax}\sqrt{\dfrac{1+bx}{1-bx}}$ , при $x=1\dfrac{1}{a}\sqrt{\dfrac{2a-b}{b}}; 0<\dfrac{b}{2}<a<b $\\ | | | \\ 69. (2.145 Сканави) | \\ $\dfrac{1-ax}{1+ax}\sqrt{\dfrac{1+bx}{1-bx}}$ , при $x=\dfrac{1}{a}\sqrt{\dfrac{2a-b}{b}}; 0<\dfrac{b}{2}<a<b $\\ | |
| | \\ 70. (2.203 Сканави) | \\ $\dfrac{(2x+\sqrt{x^2-1})\cdot\sqrt{\sqrt{\dfrac{x-1}{x+1}}+\sqrt{\dfrac{x+1}{x-1}}-2}}{(x+1)\sqrt{x+1}-(x-1)\sqrt{x-1}} $\\ | | | \\ 70. (2.203 Сканави) | \\ $\dfrac{(2x+\sqrt{x^2-1})\cdot\sqrt{\sqrt{\dfrac{x-1}{x+1}}+\sqrt{\dfrac{x+1}{x-1}}-2}}{(x+1)\sqrt{x+1}-(x-1)\sqrt{x-1}} $\\ | |
| | \\ 71. (2.210 Сканави) | \\ $\dfrac{2\sqrt{\dfrac{1}{4}\left(\dfrac{1}{\sqrt{a}}+\sqrt{a}\right)^2-1}}{2\sqrt{\dfrac{1}{4}\left(\dfrac{1}{\sqrt{a}}+\sqrt{a}\right)^2}-1-\dfrac{1}{2}\left(\sqrt{\dfrac{1}{a}-\sqrt{a}}\right)} $\\ | | | \\ 71. (2.210 Сканави) | \\ $\dfrac{2\sqrt{\dfrac{1}{4}\left(\dfrac{1}{\sqrt{a}}+\sqrt{a}\right)^2-1}}{2\sqrt{\dfrac{1}{4}\left(\dfrac{1}{\sqrt{a}}+\sqrt{a}\right)^2}-1-\dfrac{1}{2}\left(\sqrt{\dfrac{1}{a}-\sqrt{a}}\right)} $\\ | |
