| Предыдущая версия справа и слеваПредыдущая версияСледующая версия | Предыдущая версия |
| math-public:uproscheniya_s_bukvami [2020/01/16 19:27] – labreslav | math-public:uproscheniya_s_bukvami [2020/01/17 23:30] (текущий) – labreslav |
|---|
| | \\ 16. | \\ (√a−√ba√b+b√a+√a+√ba√b−b√a)⋅(√a)3⋅√ba+b−2ba−b\\ | \\ 2 | | | \\ 16. | \\ (√a−√ba√b+b√a+√a+√ba√b−b√a)⋅(√a)3⋅√ba+b−2ba−b\\ | \\ 2 | |
| | \\ 17. | \\ √xx−a2:(√x−√x−a2√x+√x−a2−√x+√x−a2√x−√x−a2)\\ | \\ a24(a2−x) | | | \\ 17. | \\ √xx−a2:(√x−√x−a2√x+√x−a2−√x+√x−a2√x−√x−a2)\\ | \\ a24(a2−x) | |
| | \\ 18. | \\ (1√a+√a+b+1√a−√a−b):(1+√a+ba−b)\\ | \\ √a−bb | | | \\ 18. | \\ (1√a+√a+b+1√a−√a−b):(1+√a+ba−b) | \\ √a−bb | |
| | \\ 19. | \\ a(√a+√b2b√a)−1+b(√a+√b2a√b)−1(a+√ab2ab)−1+(b+√ab2ab)−1\\ | \\ √ab | | | \\ 19. | \\ a(√a+√b2b√a)−1+b(√a+√b2a√b)−1(a+√ab2ab)−1+(b+√ab2ab)−1\\ | \\ √ab | |
| | \\ 20. | \\ (√a+√x√a+x−√a+x√a+√x)−2−(√a−√x√a+x−√a+x√a−√x)−2\\ | \\ a+x√ax | | | \\ 20. | \\ (√a+√x√a+x−√a+x√a+√x)−2−(√a−√x√a+x−√a+x√a−√x)−2\\ | \\ a+x√ax | |
| | \\ 26. | \\ \\ | \\ | | | \\ 26. | \\ \\ | \\ | |
| | \\ 27. (2.001 Сканави) | \\ √x+1x√x+x+√x:1x2−√x\\ | \\ x−1 | | | \\ 27. (2.001 Сканави) | \\ √x+1x√x+x+√x:1x2−√x\\ | \\ x−1 | |
| | \\ 28. (2.002 Сканави) | \\ ((√√p−√√q)−2+(√√p+√√q)−2):√p+√qp−q\\ | \\ $\dfrac{2(\sqrt{p}+\sqrt{q}^2)}{p-q} $ | | | \\ 28. (2.002 Сканави) | \\ ((√√p−√√q)−2+(√√p+√√q)−2):√p+√qp−q\\ | \\ $\dfrac{2(\sqrt{p}+\sqrt{q})^2}{p-q} $ | |
| | \\ 29. (2.003 Сканави) | \\ (√a2+a√a2−b2−√a2−a√a2−b2)22a√ab:(√ab+√ba−2);a>b>0\\ | \\ (√a+√b2)a−b | | | \\ 29. (2.003 Сканави) | \\ (√a2+a√a2−b2−√a2−a√a2−b2)22a√ab:(√ab+√ba−2);a>b>0\\ | \\ (√a+√b2)a−b | |
| | \\ 30. (2.006 Сканави) | \\ (√a+√b)2−4b(a−b):(√1b+3√1a):a+9b+6√ab√1b+√1a\\ | \\ 1ab | | | \\ 30. (2.006 Сканави) | \\ (√a+√b)2−4b(a−b):(√1b+3√1a):a+9b+6√ab√1b+√1a\\ | \\ 1ab | |
| | \\ 31. (2.007 Сканави) | \\ (√√m+√√n)2+(√√m−√√n)22(m−n):1m√m−n√n−3√mn\\ | \\ (√m−√n)2 | | | \\ 31. (2.007 Сканави) | \\ (√√m+√√n)2+(√√m−√√n)22(m−n):1m√m−n√n−3√mn\\ | \\ (√m−√n)2 | |
| | \\ 32. (2.009 Сканави) | \\ $\dfrac{2\sqrt{1+\dfrac{1}{4}\left(\sqrt{\dfrac{1}{t}}-\sqrt{t}\right)^2}}{\sqrt{1+{\dfrac{1}{4}\left(\sqrt{\dfrac{1}{t}}-\sqrt{t}\right)^2}-\dfrac{1}{2}\left(\sqrt{\dfrac{1}{t}}-\sqrt{t}\right)}} |\dfrac{t+1}{t} $ | | | \\ 32. (2.009 Сканави) | \\ 2√1+14(√1t−√t)2√1+14(√1t−√t)2−12(√1t−√t)\\ | \\ t+1t | |
| | \\ 33. (2.010 Сканави) | \\ t⋅1+2√t+42−√t+4+√t+4+4√t+4\\ | \\ −4 | | | \\ 33. (2.010 Сканави) | \\ t⋅1+2√t+42−√t+4+√t+4+4√t+4\\ | \\ −4 | |
| | \\ 34. (2.011 Сканави) | \\ (1+√x√1+x−√1+x1+√x)2−(1−√x√1+x−√1+x1−√x)2\\ | \\ 16x√x(1−x2)(x−1) | | | \\ 34. (2.011 Сканави) | \\ (1+√x√1+x−√1+x1+√x)2−(1−√x√1+x−√1+x1−√x)2\\ | \\ 16x√x(1−x2)(x−1) | |
| | \\ 47. (2.046 Сканави) | \\ √1−x2−1x(1−x√1−x2+x−1+√1+x√1+x−√1−x)\\ | \\ −1 | | | \\ 47. (2.046 Сканави) | \\ √1−x2−1x(1−x√1−x2+x−1+√1+x√1+x−√1−x)\\ | \\ −1 | |
| | \\ 48. (2.052 Сканави) | \\ (1√1−x2+1+11√1−x2−1)−2:(2−x2−2√1−x2)\\ | \\ 1−x2 | | | \\ 48. (2.052 Сканави) | \\ (1√1−x2+1+11√1−x2−1)−2:(2−x2−2√1−x2)\\ | \\ 1−x2 | |
| | \\ 49. (2.053 Сканави) | \\ (1√1−p2−√1+p2)2+2√1−p4\\ | \\ 21−p4 | | | \\ 49. (2.053 Сканави) | \\ $\left(\dfrac{1}{\sqrt{1-p^2}}-\dfrac{1}{\sqrt{1+p^2}}\right)^2+\dfrac{2}{\sqrt{1-p^4}} |\dfrac{2}{1-p^4} $ | |
| | \\ 50. (2.071 Сканави) | \\ $\dfrac{(m-1)\sqrt{m}-(n-1)\sqrt{n}}{m^2\sqrt{mn}+mn+m^2-m} |\dfrac{\sqrt{m}-\sqrt{n}}{m} $ | | | \\ 50. (2.071 Сканави) | \\ $\dfrac{(m-1)\sqrt{m}-(n-1)\sqrt{n}}{\sqrt{m^3n}+mn+m^2-m} |\dfrac{\sqrt{m}-\sqrt{n}}{m} $ | |
| | \\ 51. (2.079 Сканави) | \\ (√√m−√m2−9m+√√m+√m2−9m)2√√m24\\ | \\ √2⋅(m+3) | | | \\ 51. (2.079 Сканави) | \\ (√√m−√m2−9m+√√m+√m2−9m)2√√m24\\ | \\ √2⋅(m+3) | |
| | \\ 52. (2.081 Сканави) | \\ √t√t+2√t−2−2√t−2√t+2−4t√t2−4:√√t2−4\\ | \\ √t2−4t+2 | | | \\ 52. (2.081 Сканави) | \\ √t√t+2√t−2−2√t−2√t+2−4t√t2−4:√√t2−4\\ | \\ √t2−4t+2 | |
| | \\ 53. (2.085 Сканави) | \\ (a√a+b√b√a+√b−√ab)(√a+√ba−b)2\\ | \\ 1 | | | \\ 53. (2.085 Сканави) | \\ (a√a+b√b√a+√b−√ab)(√a+√ba−b)2\\ | \\ 1 | |
| | \\ 54. (2.086 Сканави) | \\ (a−√a2−b2a+√a2−b2−a+√a2−b2a−√a2−b2):4√a4−a2b25b2\\ | \\ 25, при a<0\\ \\ −25, при a>0 | | | \\ 54. (2.086 Сканави) | \\ $\left(\dfrac{a-\sqrt{a^2-b^2}}{a+\sqrt{a^2-b^2}}-\dfrac{a+\sqrt{a^2-b^2}}{a-\sqrt{a^2-b^2}}\right):\dfrac{4\sqrt{a^4-a^2b^2}}{(5b)^2} |25,приa<0-25,приa>0$ | |
| | \\ 55. (2.088 Сканави) | \\ $\left(\sqrt{1-x^2}+1\right):\left(\dfrac{1}{\sqrt{x+1}}+\sqrt{x-1}\right) |\sqrt{1+x} $ | | | \\ 55. (2.088 Сканави) | \\ $\left(\sqrt{1-x^2}+1\right):\left(\dfrac{1}{\sqrt{x+1}}+\sqrt{1-x}\right) |\sqrt{1+x} $ | |
| | \\ 56. (2.090 Сканави) | \\ (a−b)3(√a+√b)3+2a√a+b√ba√a+b√b+3(√ab−b)a−b\\ | \\ 3 | | | \\ 56. (2.090 Сканави) | \\ (a−b)3(√a+√b)3+2a√a+b√ba√a+b√b+3(√ab−b)a−b\\ | \\ 3 | |
| | \\ 57. (2.093 Сканави) | \\ (√3+11+√3+√t+√3−11−√3+√t)(√t−2√t+2)\\ | \\ 2√3 | | | \\ 57. (2.093 Сканави) | \\ (√3+11+√3+√t+√3−11−√3+√t)(√t−2√t+2)\\ | \\ 2√3 | |
| | \\ 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) |\dfrac{a^2}{4(a^2-x)} $ | | | \\ 58. (2.096 Сканави) | \\ √xx−a2:(√x−√x−a2√x+√x−a2−√x+√x−a2√x−√x−a2)\\ | \\ a24(a2−x) | |
| | \\ 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)} |2 $ | | | \\ 59. (2.097 Сканави) | \\ $\dfrac{\left(\sqrt{x}+2\right)\left(\dfrac{2}{\sqrt{x}}-1\right)-\left(\sqrt{x}-2\right)\left(\dfrac{2}{\sqrt{x}}+1\right)-\dfrac{8}{\sqrt{x}}}{\left(2-\sqrt{x+2}\right):\left(\sqrt{\dfrac{2}{x}+1}-\dfrac{2}{\sqrt{x}}\right)} |2 $ | |
| | \\ 60. (2.100 Сканави) | \\ (z−z√z+2−2√z)2(1+√z)2z−2+1z−z√z⋅√4z+4+z\\ | \\ z(z+1)(z+2) | | | \\ 60. (2.100 Сканави) | \\ (z−z√z+2−2√z)2(1+√z)2z−2+1z−z√z⋅√4z+4+z\\ | \\ z(z+1)(z+2) | |
| | \\ 61. (2.101 Сканави) | \\ (1a+√2−a2+4a3+2√2):(a2−1√2+1a)−1\\ | \\ −√22a | | | \\ 61. (2.101 Сканави) | \\ (1a+√2−a2+4a3+2√2):(a2−1√2+1a)−1\\ | \\ −√22a | |
| | \\ 62. (2.103 Сканави) | \\ (√ab−ab(a+√ab)−1):(2(√ab−b)(a−b)−1)\\ | \\ 0,5a | | | \\ 62. (2.103 Сканави) | \\ (√ab−ab(a+√ab)−1):(2(√ab−b)(a−b)−1)\\ | \\ 0,5a | |
| | \\ 63. (2.105 Сканави) | \\ $\left(\dfrac{1+\sqrt{1-x}}{1-x+\sqrt{1-x}}+\dfrac{1-\sqrt{1+x}}{1+x-\sqrt{1+x}}\right)^2\cdot\dfrac{x^2-1}{2}+\sqrt{1-x^2} |-1 $ | | | \\ 63. (2.105 Сканави) | \\ $\left(\dfrac{1+\sqrt{1-x}}{1-x+\sqrt{1-x}}+\dfrac{1-\sqrt{1+x}}{1+x-\sqrt{1+x}}\right)^2\cdot\dfrac{x^2-1}{2}-\sqrt{1-x^2} |-1 $ | |
| | \\ 64. (2.110 Сканави) | \\ √c−dc2√2c⋅(√c−dc+d+√c2+cdc2−cd) , при c=2,d=14\\ | \\ 13 | | | \\ 64. (2.110 Сканави) | \\ √c−dc2√2c⋅(√c−dc+d+√c2+cdc2−cd) , при c=2,d=14\\ | \\ 13 | |
| | \\ 65. (2.115 Сканави) | \\ 4ab+(1+(ab)−3)a3(√a+√b)2−2√ab−(√a+√b2b√a)−1+(√a+√b2a√b)−1(a+√ab2)−1+(b+√ab2)−1\\ | \\ (a+b)2 | | | \\ 65. (2.115 Сканави) | \\ 4ab+(1+(ab)−3)a3(√a+√b)2−2√ab−(√a+√b2b√a)−1+(√a+√b2a√b)−1(a+√ab2)−1+(b+√ab2)−1\\ | \\ (a+b)2 | |
| | \\ 66. (2.136 Сканави) | \\ 1−b√b⋅x2−2x+√b , при x=√b1−√b\\ | \\ 0 | | | \\ 66. (2.136 Сканави) | \\ 1−b√b⋅x2−2x+√b , при x=√b1−√b\\ | \\ 0 | |
| | \\ 67. (2.143 Сканави) | \\ 2b√x2−1x−√x2−1 , при $ x=\dfrac{1}{2}\left(\sqrt{\dfrac{a}{b}}+\sqrt{\dfrac{b}{a}}\right);a>0,b>0 |a-b $ | | | \\ 67. (2.143 Сканави) | \\ 2b√x2−1x−√x2−1 , при x=12(√ab+√ba);a>b>0\\ | \\ a−b | |
| | \\ 68. (2.144 Сканави) | \\ 2a√1+x2x+√1+x2 , при x=12(√ab−√ba);a>0,b>0\\ | \\ a+b | | | \\ 68. (2.144 Сканави) | \\ 2a√1+x2x+√1+x2 , при x=12(√ab−√ba);a>0,b>0\\ | \\ a+b | |
| | \\ 69. (2.145 Сканави) | \\ 1−ax1+ax√1+bx1−bx , при x=11a√2a−bb;0<b2<a<b\\ | \\ 1 | | | \\ 69. (2.145 Сканави) | \\ 1−ax1+ax√1+bx1−bx , при x=11a√2a−bb;0<b2<a<b\\ | \\ 1 | |
| | \\ 70. (2.203 Сканави) | \\ (2x+√x2−1)⋅√√x−1x+1+√x+1x−1−2(x+1)√x+1−(x−1)√x−1\\ | \\ 1√√x2−1 | | | \\ 70. (2.203 Сканави) | \\ (2x+√x2−1)⋅√√x−1x+1+√x+1x−1−2(x+1)√x+1−(x−1)√x−1\\ | \\ 1√√x2−1 | |
| | \\ 71. (2.210 Сканави) | \\ $\dfrac{2\sqrt{\dfrac{1}{4}\left(\dfrac{1}{\sqrt{a}}+\sqrt{a}\right)^2-1}}{2\sqrt{\dfrac{1}{4}\left(\dfrac{1}{\sqrt{a}}+\sqrt{a}\right)^2}-1-\dfrac{1}{2}\left(\sqrt{\dfrac{1}{a}-\sqrt{a}}\right)} |2,приa\in(0;1);\dfrac{2}{3},приa\in(1;+\infty)$ | | | \\ 71. (2.210 Сканави) | \\ $\dfrac{2\sqrt{\dfrac{1}{4}\left(\dfrac{1}{\sqrt{a}}+\sqrt{a}\right)^2-1}}{2\sqrt{\dfrac{1}{4}\left(\dfrac{1}{\sqrt{a}}+\sqrt{a}\right)^2-1}-\dfrac{1}{2}\left(\sqrt{\dfrac{1}{a}-\sqrt{a}}\right)} |2,приa\in(0;1);\dfrac{2}{3},приa\in(1;+\infty)$ | |
| | \\ 72. (2.216 Сканави) | \\ (√m+2m−2+√m−2m+2):(√m+2m−2−√m−2m+2)\\ | \\ 0,5m | | | \\ 72. (2.216 Сканави) | \\ (√m+2m−2+√m−2m+2):(√m+2m−2−√m−2m+2)\\ | \\ 0,5m | |
| | \\ 73. (2.218 Сканави) | \\ √x+2√2x−4+√x−2√2x−4\\ | \\ 2√2 | | | \\ 73. (2.218 Сканави) | \\ √x+2√2x−4+√x−2√2x−4\\ | \\ 2√2 | |
