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  1. 1. . , . 2014 (e-book) CD-ROM (ISBN 978-960-16-4244-4) . Copyright . ( ), , , 2004 2014. , .
  2. 2. (. 2121/1993 ) . (, ) , , , , , .
  3. 3. . , . , 3 2o 474 8 477 9 478 10 480 11 481 12 483 13 484 14 485 15 486 16 487 17 488 18 489 19 490 20 491 21 492 22 493 23 495 24 496 25 497 26 498 27 499 28 503 29 504 30 505 31 506 32 507 33 508 34 509 35 510 36 936 37 938 38 944 39 947 40 950 41 952 42 955 43 991 44 996 45 999 46 1003 47 1005 48 1007 49 1009 50 1015 51 1024 52 1032 53 1039 54 1042 55 1050 56 1055 57 1057 58 1062 59 1064 60 1067 61 1070 62 1074 63 1077 64 1080 65 1082 66 1086 67 1088 68 1089 69 1090 70 1091 71 1092 72 1093 73 1096 74 1097 75 1100 76 1101 77 1102 78 1273 79 1275 80 1276 81 1277 82 1278 83 1281 84 1282 85 1283 86 1287 87 1288 88 1293 89 1297 90 1298 91 1300 92 1301 93 1302 94 1305 95 1506 96 1509 97 1512 98 1513 99 1520 100 1529 101 1532 102 1533 103 1537 104 1541 105 1542 106 1544 107 1553 108 2212 109 2702 110 3378 111 3379 113 3380 115 3381 116 3382 117 3383 118 3384 119 3828 120 3839 121 3847 122 3852 123 3857 124 3863 125 3870 126 3874 127 3878 128 3884 129 4288 130 4290 131 4295 132 4299 133 4300 134 4301 135 4302 136 4303 137 4304 138 4305 139 4306 140 4308 141 4309 142 4310 143 4311 144 4312 145 4313 146 4314 147 4315 148 4316 149 4317 150 4318 151 4319 152 7518 153 7519 154 7520 155 7521 156 8173 157
  4. 4. . , . , 4 4o 1868 159 1874 160 1880 162 1890 163 1936 164 1955 166 1963 168 2046 169 2047 171 2052 172 2055 173 2064 174 2073 175 2080 176 2081 177 2083 178 2084 179 2220 180 2226 182 2229 184 2234 186 2238 187 2244 188 2255 189 2273 190 2287 191 2301 192 2302 193 2323 194 2332 195 2336 196 2338 198 2339 199 2340 201 4542 203 4545 204 4548 205 4551 206 4558 207 4575 208 4607 209 4629 211 4647 213 4654 215 4656 216 4657 217 4659 219 4660 220 4663 221 4665 222 4667 223 4671 224 4679 225 4680 226 4681 227 4682 228 4819 229 4833 230 4835 231 4836 232 4853 233 4857 235 4858 236 4859 237 4861 238 4862 240 4886 241 4903 243 4912 244 4925 245 4946 246 4952 247 4957 248 4962 249 4970 250 4975 251 4992 252 5275 254 5285 255 5316 256 5317 257 5322 258 5879 259 5882 261 5884 263 5885 264 6143 265 6144 267 6146 269 6223 271 6224 272 6226 274 6227 276 6228 277 6229 278 6231 280 6678 282 6859 283 7263 284 7502 285 7503 287 7504 288 7506 289 7510 290 7511 292 7512 294 7514 295 7515 296 7516 297 7517 298 7677 299 7684 300 7745 301 7784 302 7791 304 7940 305 7958 306 7974 308 8170 309 8217 311 8443 313 8445 314 8448 315 8451 317 8453 318 8455 319 8458 320 10774 321 10775 323
  5. 5. . , . , 5 2 2 497 499 1003 1102 1287 1.2 4 1506 1520 3383 3384 3878 2.1 5 1070 1080 3874 486 487 506 1092 1541 2.2 6 3852 3870 4299 7519 7520 504 509 996 1009 1089 2.3 7 1091 2702 3884 936 938 944 947 950 952 955 1276 1300 43112.4 8 4314 4316 8173 3.1 9 485 507 1055 3382 4302 481 483 493 496 1005 1007 1093 1097 1275 1281 1282 1298 1509 1533 3839 3847 3857 3863 4308 4309 3.3 11 4310 4313 4317 7518 489 491 503 505 991 1039 1062 1074 1077 1273 1305 4290 4295 4305 4306 4.1 12 4318 7521 478 484 490 498 1067 1277 1278 1288 1297 15124.2 13 1544 3380 474 480 508 1015 1050 1057 1064 1086 1101 1301 1513 4300 4301 4303 4304 5.2 16 4312 4319 495 1032 1088 1100 3828 5.3 17 4288 4315 488 510 999 1042 1082 6.1 19 1302 1532 1537 477 492 1024 1090 1542 6.2 20 1553 3381 1096 1283 1293 1529 2212 6.3 21 3378 3379
  6. 6. . , . , 6 4 4 1868 1936 2064 2073 2080 1.2 4 6144 2.3 2301 3.1 2302 1955 2332 4551 4558 4654 4659 4665 4667 4857 4903 4957 4962 4970 4975 4992 5317 6223 6224 6231 7510 3.3 11 7515 7516 7940 1890 2081 2238 2287 4833 4835 4946 4952 7263 77914.1 12 8443 8453 1874 2055 2244 2255 2273 2336 4542 4548 4607 4663 4680 4681 4682 4819 4834 4836 4853 4859 5285 5322 5884 5885 6226 6227 7677 4.2 13 7684 7958 7974 8445 8455 2047 2083 2323 4671 4858 4925 6143 7503 7504 75145.2 16 8458 10775 5.3 17 2340 4629 6678 6859 8170 2052 2084 2220 2226 2229 2234 4545 4575 4861 4862 5879 6228 7506 7511 7512 6.1 19 7517 7745 8217 1963 2338 4656 4660 4679 4886 4912 5275 5882 61466.2 20 8448 8451 1880 2046 2339 4647 4657 6.3 21 6229 7502 7784 10774 1.2 326 2.1 330 2.2 331 2.3 333 2.4 335 3.1 337 3.3 338 4.1 347 4.2 352 5.2 362 5.3 367 6.1 370 6.2 377 6.3 383
  7. 7. 2014 2
  8. 8. . , . , 88 , 16 . . . GI_A_ALG_2_474 ( ) : 1, 3, 5, 7, ) ( ) - . ( 15) ) . ( 10) : 5.2 : ) 2 1 3 2 4 3 2 = = = , * , ,N = 2 1 1= . * 1 ( 1) 1 ( 1) 2 1 2 2 2 1, = + = + = + = N . 100 2 100 1 200 1 199= = = , 199. ) * , ,N : ( ) ( )1 2 * 2 1 2 1 1 2 2 2 2 S , 2 2 2 + + + = = = = N , .
  9. 9. . , . , 99 , 11, 19, 20 . . . GI_A_ALG_2_477 f, 2 x 5x 6 f(x) x 3 + = . ) f. ( 7) ) f. ( 9) ) f xx yy . ( 9) : 3.3, 6.1, 6.2 : ) x 3 0 x 3, fA {3} ( , 3) (3, )= = + R . ) 2 x 5x 6 + ( ) 2 5 4 1 6 1= = ( ) 5 1 6 3 5 1 5 1 2 2x 5 1 42 2 2 2 2 + = = = = = = = , 2 x 5x 6 (x 2)(x 3) + = . x {3} R 2 x 5x 6 (x 2)(x 3) f(x) x 2 x 3 x 3 + = = = . ) fC yy x = 0, : f(0) = 0 2 = 2, (0, 2). fC xx y = 0, x 3: f(x) = 0 x 2 = 0 x = 2 (), (2, 0).
  10. 10. . , . , 1010 , 11, 13 . . . GI_A_ALG_2_478 : ( )2 2 x x 1 0 + + = (1), . ) , (1) . ( 12) ) : 2 S P 2 0 , S P - (1). ( 13) : 3.3, 4.2 : ) ( )2 2 x x 1 + + ( ) ( )2 2 2 2 2 4 1 4 4 4 3 4 4= + = + = + . , 0, 2 3 4 4 0 + (). 2 3 4 4 + ( ) ( ) 2 4 4 3 4 64= = , ( ) ( ) 4 8 12 2 4 64 4 8 6 6 4 8 4 22 3 6 6 6 3 + = = = = = = = : + 2 2 3 2 3 4 4 + + 2 () 2 3 . ) 2 2, 3 , Vieta 1 2x , x (1), : 1 2 S x x 1 = + = = 2 2 1 2 1 P x x 1 1 + = = = + . : 2 S P 2 0 2 2 ( 1) 2 0 + 2 2 1 2 0 + 2 1 1 1 . 1 2 2, 3 , [2, 1]. + 2 1 2 3
  11. 11. . , . , 1111 , 16 . . . GI_A_ALG_2_480 . 7 36 300. ) ; - . ( 12) ) ; ( 13) : 5.2 : ) , * , ,N 10, = 1 . ) ( ) ( ) * 1 1 1 1 , ,= + = + N 10. 7 = 36, : ( )1 7 1 36+ = 1 6 36+ = (). * , ,N 10, : ( ) ( )1 1 * 2 1 2 1 S , , 2 2 + + = = N 10. : 10S 300= ( )12 10 1 10 300 2 + = 15(2 9) 300+ = 12 9 60+ = (). (), () : 1 1 6 36 2 9 60 + = + = 1 1 2 12 72 2 9 60 = + = 1 12 9 72 60 2 9 60 + = + + = 1 3 12 2 60 9 = = 1 4 2 60 9 4 = = 1 4 2 24 = = 1 4 12 = = . : 12, 16, 20, 24, 28, 32, 36, 40, 44, 48.
  12. 12. . , . , 1212 , 11 . . . GI_A_ALG_2_481 ( )2 x 2x 4 1 0 + = , . ) . ( 8) ) . ( 8) ) 1 2x ,x , : 1 2 1 2x x x x+ = . ( 9) : 3.3 : ) ( )2 x 2x 4 1 + ( ) ( ) ( ) ( ) 2 22 2 2 4 1 4 1 4 16 16 4 4 4 4 2= = + = + = . ) ( ) 2 2 0 0 , ( )2 x 2x 4 1 0 + = . ) Vieta 1 2x , x ( )2 x 2x 4 1 0 + = , : 1 2 2 S x x 2 1 = + = = 1 2 4( 1) P x x 4 4 1 - -= = = . : x x x x1 2 1 2+ =+ =+ =+ = 2 = 4 4 2 4 = 4 2 = 4 = 2.
  13. 13. . , . , 1313 , 7, 9, 11 . . . GI_A_ALG_2_483 ) 2x 1 3 = . ( 12) ) , < (), 2 x x 3 0+ + = . ( 13) : 2.3, 3.1, 3.3 : ) 2x 1 3 = 2x 1 = 3 2x 1 = 3 2x = 1 + 3 2x = 1 3 2x = 4 2x = 2 x = 2 x = 1. ) , 2x 1 3 = , 2 1. , < , = 1 = 2. 2 x x 3 0+ + = 2 x 2x 3 0 + + = (). 2 x 2x 3 + + ( )2 2 4 1 3 16= = 2 4 2 1 2 16 2 4 2 2x 2 4 62 ( 1) 2 3 2 2 + = = = = = = = . () x = 1 x = 3.
  14. 14. . , . , 1414 , 12, 13 . . . GI_A_ALG_2_484 ) : 2x 5 3 2 2x x 1 0 . ( 16) ) ). ( 9) : 4.1, 4.2 : ) 2x 5 3 3 2x 5 3 5 3 2x 3 + 5 2 2x 8 1 x 4. 2 2x x 1 2 ( 1) 4 2 ( 1) 9= = , 1 3 2 1 ( 1) 9 1 3 4 4 2x 1 3 42 2 4 1 4 4 = = = = = + = = : + 1 2 1 x 2 2x x 1 + + 2 2x x 1 0 [ ) 1 x , 1, 2 + . ) : + 1 2 1 4 x[1, 4].
  15. 15. . , . , 1515 , 9 . . . GI_A_ALG_2_485 2 x x 1= + , . ) : ( )( ) ( 1 x 1 , 1) = + . ( 8) ) , . ( 8) ) ; . ( 9) : 3.1 : ) : 2 x x 1= + 2 x x 1 = ( )( ) ( 1 x 1 , 1) = + . 1 0 1 ( )( ) ( 1 x 1)1 = + ( )( ) 1 1 x 1 1 + = = + . = 1 ( )( ) ( 1 x 1)1 = + : (1 1)x = (1 1)(1 + 1) 0x = 02 0x = 0, . ) , ( ) 1 x 1 ( ) ( ) ,1 , = + - 1 x 1= + . ) , ( ) 1 x 1 ( ) ( ) ,1 , = + - = 1.
  16. 16. . , . , 1616 , 6 . . . GI_A_ALG_2_486 0 < < 1, : ) : 3 < . ( 13) ) : 3 1 0, ,1, , . ( 12) : 2.2 : ) 0 < < 1, > 0 + 1 > 0 + 1 + 1 > 1, + 1 > 0. , 0 < < 1 0 1 < 1 < 1 1 1 < 1 < 0, 1 < 0. 3 2 ( 1) ( 1)( 1) 0 = = + < , 3 < . ) 3 1 0 1 < < < < . : 3 0 < , > 0, 3 < , () , < 1, , 1 1 < , < 1 1 1 1 > 1 1 > .
  17. 17. . , . , 1717 , 5, 6 . . . GI_A_ALG_2_487 ) x, y : ( ) ( ) 2 2 2 2 x 1 y 3 x y 2x 6y 10 + + = + + + . ( 12) ) x, y : 2 2 x y 2x 6y 10 0+ + + = . ( 13) : 2.1