| Номер | ——— Условие ——— | ——— Ответ ——— |
|---|---|---|
| 1. | (√a√a−√b−√b√a+√b)⋅a−ba2+ab | 1a |
| 2. | (√a+1√a−1−√a−1√a+1+4√a)(√a4−1√4a) | 2a |
| 3. | (√a√a+√b+√b√a−√b+2√aba−b)(√a−√ab+b√a+√b) | √a+√b |
| 4. | 2a√a+b+√a−b1+√a−ba+b⋅2b(a+b)√a+b−(a−b)√a−b | 1 |
| 5. | a√a+b√b√a+√ba−b+2√b√a+√b−√aba−b | 1 |
| 6. | a−ba+b+√(a+b)2−(a−b)2+2(a√a−b√b)(√a+√b)(a+b−√(a+b)2−(a−b)2) | 3a+3ba−b |
| 7. | √3b+a32a+√3ab−√3b+a32a−√3ab , при 0<a3<3b | a√2 |
| 8. | √z−24z−16√z+16:(√z2√z−4−z−122z−8−2z+2√z) | √z4(√z+2) |
| 9. | (√a−√b)3+2a2√a+b√ba√a+b√b+3√ab−3ba−b | 3 |
| 10. | (1√y−2√x+√y):(√x−x+y√x+√y)⋅√y | 1√y |
| 11. | (√c+√d−2√cd√c+√d):(√c−√d√c+√d+√d√c)⋅√c | c |
| 12. | ((√ab−√ba):(√ab+√ba−2)):(1+√ba) , при a>0,b>0 | √a√a−√b |
| 13. | (1+√1−x1−x+√1−x+1−√1+x1+x−√1+x)2⋅x2−12+1 , при 0<x<1 | √1−x2 |
| 14. | (√a+1√ab+1+√ab+√a√ab−1−1):(√a+1√ab+1−√ab+√a√ab−1+1) | −√ab |
| 15. | (2+√aa+2√a+1−√a−2a−1)⋅a√a+a−√a−1√a | 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) |
| 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 |
| 20. | (√a+√x√a+x−√a+x√a+√x)−2−(√a−√x√a+x−√a+x√a−√x)−2 | a+x√ax |
| 21. | x−y√x+√y:((√√x−√√y)−1+(√√x+√√y)−1)−2 | 4√x√x−√y |
| 22. | (1(√a+√b)−2−(√a−√ba√a−b√b)−1):√ab | 1 |
| 23. | √(√a+b√a3−b3)−1⋅a−b2a+b√a+b2−√a , при √a>b | −b |
| 24. | (√a−2a+2√a+√a+2a−2√a)⋅(√a)3a+4−8a−4 | 2 |
| 25. | (√x−1√x+1+√x−1+x−1√x2−1−x+1)1√x2−1 | 1 |
| 26. | | |
| 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 | 2(√p+√q)2p−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 |
| 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 |
| 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 |
| 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) |
| 35. (2.012 Сканави) | x−1x+√x+1:√x+1x√x−1+21√x | x+1 |
| 36. (2.013 Сканави) | (1√a+√a+1+1√a−√a−1):(1+√a+1√a−1) | √a−1 |
| 37. (2.021 Сканави) | 4x(x+√x2−1)2(x+√x2−1)4−1 | 1√x2−1 |
| 38. (2.022 Сканави) | √(x+2)2−8x√x−2:√x | −√x, при x∈(0,2); √x, при x∈(2,+∞) |
| 39. (2.028 Сканави) | x⋅1√x2−a2+1a⋅1√x−a+√x−a:a2√x+ax−√x2−a2+1x2−ax | 2x2−a2 |
| 40. (2.032 Сканави) | √abc+4a+4√bca√abc+2 , при a=0,04 | 5 |
| 41. (2.033 Сканави) | (2p+1)√2p+1+(2p−1)√2p−1√4p+2√4p2−1 | 4p−√4p2−1 |
| 42. (2.034 Сканави) | 1−1√a−1−√a+11√a+1−1√a−1:√a+1⋅√a2−1(a−1)√a+1−(a+1)√a−1 | √a2−1 |
| 43. (2.037 Сканави) | 1−1x2√x−1√x−2x√x+1x2−x√x−1√x | −√x(1+2x2) |
| 44. (2.038 Сканави) | (√a2−12√a)2(√a−1√a+1−√a+1√a−1) | 1−a√a |
| 45. (2.041 Сканави) | 12(1+√a)+12(1−√a)−a2+21−a3 | −1a2+a+1 |
| 46. (2.044 Сканави) | (√x−a√x+a+√x−a+x−a√x2−a2−x+a):√x2a2−1;x>a>0 | 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 |
| 49. (2.053 Сканави) | (1√1−p2−1√1+p2)2+2√1−p4 | 21−p4 |
| 50. (2.071 Сканави) | (m−1)√m−(n−1)√n√m3n+mn+m2−m | √m−√nm |
| 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 |
| 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−a2b2(5b)2 | 25, при a<0 −25, при a>0 |
| 55. (2.088 Сканави) | (√1−x2+1):(1√x+1+√1−x) | √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 |
| 57. (2.093 Сканави) | (√3+11+√3+√t+√3−11−√3+√t)(√t−2√t+2) | 2√3 |
| 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) | (√x+2)(2√x−1)−(√x−2)(2√x+1)−8√x(2−√x+2):(√2x+1−2√x) | 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 |
| 62. (2.103 Сканави) | (√ab−ab(a+√ab)−1):(2(√ab−b)(a−b)−1) | 0,5a |
| 63. (2.105 Сканави) | (1+√1−x1−x+√1−x+1−√1+x1+x−√1+x)2⋅x2−12−√1−x2 | −1 |
| 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 |
| 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=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 |
| 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 |
| 71. (2.210 Сканави) | 2√14(1√a+√a)2−12√14(1√a+√a)2−1−12(√1a−√a) | 2, при a∈(0;1); 23, при a∈(1;+∞) |
| 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 |
| 74. (2.233 Сканави) | 1√a−1−√a+11√a+1−1√a−1:√a+1(a−1)√a+1−(a+1)√a−1−(1−a2) | √a2−1 |
| 75. (2.236 Сканави) | √z2−1√z2−1−z , при z=12(√m+1√m) | m−12m, при m∈(0;1) 1−mm, при m∈[1;+∞) |
| 76. (2.279 Сканави) | a+b(√a−√b)2(3ab−b√ab+a√ab−3b312√14(ab+ba)2−1+4ab√a+9ab√b−9b2√a32√b−2√a) , при a>b>0 | −2b(a+3√ab) |
| 77. (2.280 Сканави) | 2a(a+2b+√a2+4ab)(a+√a2+4ab)(a+4b+√a2+4ab) | √aa+4b |
| 78. (2.282 Сканави) | (√1+x√1+x−√1−x+1−x√1−x2−1+x)(√1x2−1−1x) , при 0<x<1 | −1 |