kimyo uchun matematika

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4 al-xorazmiyning ajoyib tenglamasi matematik olim al-xorazmiydan inson haqida so'rashganda olim shunday dedi : agar inson chiroyli xulq sohibi bo'lsa, u 1 ga teng agar chiroy sohibi bo'lsa, 1 ning yoniga 0 ni qo'sh =10 bo'ladi agar u boy bo'lsa, yana bir 0 ni qo'sh = 100 bo'ladi agar nasl–nasabli bo'lsa, yana bir 0 ni qo'sh = 1000 bo'ladi agar 1 raqami yo'q bo'lib ketsa, faqat 000 qoladi va ular hech qanday qiymatga ega bo'lmay qoladi !! 5 yaxlitlash usulida bir–biriga qo'shish qiyin bo'lgan sonlarni qo'shishni osonlashtiradigan sonlarga aylantiriladi. bunda yaxlitlash qarama-qarshi tomonga bo'ladi. ya'ni yaxlitlangan son qo'shish orqali bo'lgan bo'lsa → natijadan huddi shuncha ayiramiz, agar ayirish orqali bo'lgan bo'lsa → natijaga huddu shuncha qo'shamiz 138 150 masalan (1) : 288 + 138 + 155 = 293 + 5 293 x1 y1 x2 y2 + − 1) bizga 155 noqulay son bo'lgani uchun 155 dan 5 ni ayirib 150 …

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son 100 ga yaxlitlaymiz + 𝟓 2) biz 95 ga qo'shgan 5 ni endi ayiramiz. masalan (4) : 187 + 95 = 282 182 + 100 = 282 − 𝟓 8 qo’shuv (+) 1-12 bosqich no 1-bosqich 2-bosqich 3-bosqich 4-bosqich 5-bosqich 6-bosqich 1 11+7= 29+14= 37+23= 35+36= 42+60= 113+115= 2 8+6= 23+17= 17+18= 33+43= 54+72= 125+102= 3 12+5= 18+27= 31+32= 56+31= 72+74= 109+112= 4 8+14= 10+24= 22+42= 25+55= 59+30= 146+70= 5 12+8= 28+29= 33+20= 42+26= 69+47= 116+93= 6 5+6= 13+25= 37+25= 48+21= 50+69= 80+144= 7 12+8= 15+24= 22+29= 51+52= 42+69= 114+79= 8 5+13= 19+10= 30+20= 40+23= 31+52= 79+127= 9 6+13= 18+10= 30+29= 21+30= 30+51= 120+90= 10 14+13= 13+21= 25+41= 52+31= 61+28= 109+149= 11 8+11= 18+22= 32+20= 25+43= 27+30= 145+135= 12 6+12= 12+16= 41+15= 58+28= 28+45= 98+74= 13 14+6= 26+22= 32+38= 41+41= 61+69= 104+88= 14 14+9= 11+17= 24+40= 38+34= 48+46= 139+100= 15 10+7= 17+28= 20+34= 44+22= 27+42= 136+123= no 7-bosqich 8-bosqich …

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+1008= 1073+1019= 1102+1026= 4 589+650= 939+890= 625+670= 848+899= 1091+836= 5 474+511= 837+940= 690+572= 703+572= 1078+999= 6 685+499= 620+840= 745+763= 1044+646= 703+1202= 7 607+775= 875+500= 645+725= 963+570= 890+610= 8 743+521= 463+895= 565+695= 837+594= 1037+991= 9 681+835= 519+714= 723+640= 799+749= 631+728= 10 687+537= 664+824= 946+855= 1072+827= 1060+852= 11 580+662= 807+759= 939+691= 838+765= 1009+646= 12 511+434= 604+769= 881+864= 1034+881= 1011+1104= 13 404+408= 809+797= 874+746= 632+823= 1222+619= 14 485+722= 744+935= 679+557= 635+681= 836+710= 15 752+771= 773+583= 615+812= 711+1014= 641+1151= no 18-bosqich 19-bosqich 20-bosqich 21-bosqich 22-bosqich 1 1154+1295= 1224+1130= 1053+832= 1425+1395= 1125+1182= 2 812+920= 1158+1104= 810+1356= 460+1613= 1103+1273= 3 1095+1120= 1386+1177= 786+889= 1068+1317= 1018+1551= 4 1109+689= 926+1395= 1436+1025= 1119+1109= 1749+1156= 5 959+1205= 1296+853= 1147+1482= 1311+1034= 1476+1695= 6 674+1270= 895+1181= 1103+1099= 1451+1213= 1692+1458= 7 655+873= 1410+1325= 899+1532= 859+1622= 1050+1240= 8 1247+746= 1080+987= 1467+1040= 833+1309= 911+1732= 9 1218+1219= 1023+841= 1481+974= 1257+1587= 1632+1636= 10 976+1157= 723+1245= 902+1138= 1299+1004= 1390+1121= 11 1258+767= 1447+706= 986+855= 1491+1034= 1377+1724= 12 1166+1131= 851+1387= …

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92+1356= 1220+1238= 9 1357+890= 1611+1023= 1947+1687= 1783+1707= 2062+1975= 10 1375+1684= 1261+1888= 1739+1794= 1123+1647= 2105+1294= 11 1060+1018= 1713+1293= 1567+1170= 1417+2039= 2074+1309= 12 1538+1215= 1631+1415= 1950+1305= 1717+1315= 1402+1423= 13 894+905= 1778+1499= 1504+1536= 1263+1211= 1495+1679= 14 1647+1028= 1138+1117= 1424+1684= 1530+1374= 1461+2097= 15 1279+1622= 1574+1642= 2001+1403= 1833+1285= 1586+1792= no 28-bosqich 29-bosqich 30-bosqich 31-bosqich 32-bosqich 1 2344+2028= 1779+2374= 1691+2184= 1652+1346= 2654+1476= 2 1928+1856= 1982+2230= 1993+2512= 1986+2288= 1847+2475= 3 1994+2250= 2120+1390= 2278+2041= 2173+1629= 2398+1423= 4 1192+1605= 2004+1460= 2113+2084= 2105+1787= 2056+2575= 5 2197+1196= 1963+1906= 2122+1262= 2520+1743= 2478+1888= 6 1789+1617= 2198+1769= 1481+2299= 2184+1750= 2190+2571= 7 1226+1931= 1558+2243= 1978+2502= 1614+1472= 1438+2331= 8 2211+1560= 1921+2022= 2546+2458= 1562+1869= 1844+2527= 9 1462+1567= 2436+1954= 2135+2201= 2035+1458= 1359+2386= 10 1490+1787= 1790+2200= 1272+1363= 3433+2178= 2517+2728= 11 2239+2129= 1210+2245= 2058+1494= 1465+1364= 2093+2643= 12 1327+2184= 2154+2126= 2533+2392= 1658+1752= 2642+1509= 13 2043+1443= 2265+2043= 2415+1506= 1354+2409= 2109+1369= 14 1517+1195= 1974+1657= 2548+1461= 1384+2226= 2128+2400= 15 1186+2219= 2373+2126= 1503+2395= 2453+1379= 1580+2330= 11 qo’shuv (+) 33-42 -bosqich no 33-bosqich 34-bosqich 35-bosqich 36-bosqich …

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11 2189+2439= 1999+2778= 2399+2770= 2749+2036= 2653+2617= 12 2595+1833= 1758+1547= 2099+2239= 2699+2369= 2700+1794= 13 2163+1791= 2254+2728= 2649+2820= 2919+2401= 2457+3046= 14 2662+2082= 2279+2726= 3019+2904= 3131+2343= 2680+2228= 15 1435+1674= 2694+2373= 2409+2913= 2746+2870= 3015+1724= no 38-bosqich 39-bosqich 40-bosqich 41-bosqich 42-bosqich 1 3247+2770= 3438+2732= 2161+3390= 1840+3190= 2058+2583= 2 2634+2020= 2047+1733= 2248+3442= 2972+3143= 3386+3174= 3 2941+2801= 3155+2785= 2332+2158= 2022+2649= 2656+2315= 4 1890+2770= 2283+1838= 3217+1758= 2519+3061= 2277+2637= 5 2259+3257= 3121+3341= 2916+2089= 2909+3401= 2001+3658= 6 2589+2137= 2557+2441= 2311+2062= 3157+1992= 2895+1949= 7 2348+3270= 2011+2549= 2089+2949= 2739+2533= 2380+2885= 8 2415+2225= 1949+3371= 3133+2085= 3341+2071= 3274+2938= 9 2160+2879= 1949+3371= 2052+2404= 1805+3604= 2201+2558= 10 2572+2711= 2789+1780= 3022+2620= 3529+3335= 3463+3679= 11 2874+2315= 2542+3144= 2183+2367= 2110+3618= 3444+2768= 12 2886+2281= 2119+2346= 2699+1885= 2418+2290= 2970+3729= 13 2996+3208= 3400+3427= 3280+3147= 3102+2292= 3519+3391= 14 3089+3219= 3430+2917= 3156+1824= 3275+3388= 2000+2409= 15 1951+2983= 1805+2341= 2077+3023= 2901+2863= 2137+2891= 12 qo’shuv (+) 43-52 -bosqich no 43-bosqich 44-bosqich 45-bosqich 46-bosqich 47-bosqich 1 2164+3735= 3370+2717= 3334+2783= 2921+3602= 3328+2722= 2 3524+1993= 2696+2302= 2266+2915= 4003+2284= 3761+2449= 3 …

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4 al-xorazmiyning ajoyib tenglamasi matematik olim al-xorazmiydan inson haqida so'rashganda olim shunday dedi : agar inson chiroyli xulq sohibi bo'lsa, u 1 ga teng agar chiroy sohibi bo'lsa, 1 ning yoniga 0 ni qo'sh =10 bo'ladi agar u boy bo'lsa, yana bir 0 ni qo'sh = 100 bo'ladi agar nasl–nasabli bo'lsa, yana bir 0 ni qo'sh = 1000 bo'ladi agar 1 raqami yo'q bo'lib ketsa, faqat 000 qoladi va ular hech qanday qiymatga ega bo'lmay qoladi !! 5 yaxlitlash usulida bir–biriga qo'shish qiyin bo'lgan sonlarni qo'shishni osonlashtiradigan sonlarga aylantiriladi. bunda yaxlitlash qarama-qarshi tomonga bo'ladi. ya'ni yaxlitlangan son qo'shish orqali bo'lgan bo'lsa → natijadan huddi shuncha ayiramiz, agar ayirish orqali bo'lgan bo'lsa → natijaga huddu shuncha qo'shamiz 138 150 masalan (1) …

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