Buxoro davlat universiteti qosimov f. M. Qosimova m. M

8. “Butun sonlar va ular ustida amallar” mavzusida topshiriqlar.
Amal komponentlari va natijasi orasidagi bog’lanishlardan foydalanib quyidagi tenglamalarni yeching.
1) 180-{[(30∙x+10):5-15]∙4+30}:2=155
2) 384-{[(12:x+18)∙2-12]:3+24}∙3=294
3) 246-{[(32+28:x):9+26]∙4+26}∙2=292
4) 504-{[(x+12∙4)∙2-30]:15+86}∙3=234
5) {[(12∙x+12):4+35]∙5-120}:26+150=155
6) {[(18∙x+14):2+75]∙2-180}:4+165=170
7) {[(16+2∙x)∙4+20]:5-160}:7+180=160
8) {[(160-3∙x):10+90]∙3-180}:6+180=200
9) {[130+(25+3∙x)∙2]:4+120}:7+120=140
10) {[(260-13∙x):5+21]∙4-140}:5+120=140
11) {[(330-15∙x):5+42]:2-21}:3+110=120
12) 246+{[(12-x∙3)∙5+70]:5-12}∙32=502
13) 184+{[(180-30∙x):3+70]:2+45}∙2=384
14) 192+{[(200-33∙x)∙3+67]:10+23}∙5=492
15) 108+{[(108-52∙x)∙5+84]:4+24}∙3=258
16) 224-{[(64:(2∙x)+26)∙5-46]:4+44}=154
17) [168:(44-2∙x)+16]:5+84=104
18) [144:(56-3∙x)+18]:5+74=94
19) 1264: {[(16+2∙x)∙4-14]:5+266}=4
20) {[108+3∙(x+102)]:4+13}∙2-144=96
21) {[(120-14∙x):4+127]∙3-225}:5+55=100
22) {[(360-12∙x):6+42]:2+49}:5+120=140
23) {[(384+11∙x):4+13]:4+30}∙5=300
24) {[(146-2∙x):5+120]∙2+20}:5=60
25) {[(254-3∙x):4+184]:2+13}∙3-94=296
26) {[(32:x+166):2+15]∙3-126}:87+108=110
27) 254-{[(12∙x-18):2+114]∙3-310}:4=204
28) 118-{[(15∙x-32):2+111]∙3-410}:4=163
29) 180:{[(60-2∙x)∙5+140]:2-100}+116=120
30) 200:{[(80-4∙x)∙5+64]:2+28-100}+108=110
9. “Rasional sonlar. Haqiqiy va kompleks sonlar” mavzulariga doir topshiriqlar.

1) Musbat ratsional sonlarni ko’paytirish amali assotsiativlik xossasiga ega ekanligini isbotlang.

2) Musbat ratsional sonlarni ko’paytirish amali kommutativlik xossasiga ega ekanligini isbotlang.
3) Musbat ratsional sonlarni qo’shish amali kommutativlik xossasiga ega ekanligini isbotlang.
4) Musbat ratsional sonlarni ko’paytirish qo’shishga nisbattan distributivlik xossasiga ega ekanligini isbotlang.
5) Musbat ratsional sonlarni ko’paytirish ayirishga nisbatan distributivlik xossasiga ega ekanligini isbotlang.
6) Istalgan musbat ratsional son a,b,c lar uchun (a+c=b+c) (a=b) bajarilishini isbotlang.
7) Musbat ratsional sonlar uchun “katta” munosabati ta’rifini tuzing va munosabat tranzitiv ekanligini isbotlang.
8) Musbat ratsional sonlar uchun “kichik” munosabati ta’rifini tuzing va munosabat tranzitiv ekanligini isbotlang.
9) Musbat ratsional sonlar uchun “katta” munosabati ta’rifini tuzing va bu munosabat antisimmetrik ekanini isbotlang.
10) Istalgan musbat ratsional son a va b lar uchun a+b>a bajarilishini isbotlang.
11) Nima uchun va kasrlarni chekli o’nli kasr ko’rinishida yozib bo’lmaydi. Javobingizni asoslab byering.
12) Quyidagi kasrlardan qaysilarini chekli o’nli kasr ko’rinishida tasvirlab bo’ladi? , javobingizni izohlang.
13) Quyidagi kasrlardan qaysilari chekli o’nli kasr ko’rinishida tasvirlab bo’ladi? . Javobni izohlang.
14) kasrlardan qaysilarini chekli o’nli kasr ko’rinishida yozish mumkin? Javobingizni izohlang.
15) Qisqarmas kasrni qachon chekli o’nli kasr ko’rinishida yozish mumkin? Javobingizni asoslab bering. Misollar keltiring.
16) Qachon qisqarmas oddiy kasrni cheksiz davriy o’nli kasr ko’rinishida tasvirlash mumkin? Javobingizni asoslab byering. Misollar keltiring.
17) Sof davriy o’nli kasr qanday oddiy kasrga teng. Javobingizni asoslang. Misollar keltiring.
18) Aralash davriy o’nli kasr qanday oddiy kasrga teng? Javobingizni asoslang. Misollar keltiring.
19) Kvadrati uchga teng bo’lgan musbat ratsional son mavjud emasligini isbotlang.
20) Ratsional son q bilan irratsional son ning yig’indisi har doim irratsional son bo’lishini isbotlang.
21) yig’indining 0,001 gacha aniqlikda olingan taqribiy qiymatini toping.
22) yig’indining 0,001 gacha aniqlikda olingan taqribiy qiymatini toping.
23) yig’indining 0,001 gacha aniqlikda olingan taqribiy qiymatini toping.
24) ko’paytmaning 0,1 gacha aniqlikda olingan taqribiy qiymatini toping.
25) ko’paytmaning 0,1 gacha aniqlikda olingan taqribiy qiymatini toping.
26) ko’paytmaning 0,001 gacha aniqlikda olingan taqribiy qiymatini toping.
27) va e = 2,71828.. sonlarning yig’indisini 0,01 aniqlikda toping.
28) va e = 2,71828.. sonlarning ko’paytmasini 0,01 aniqlikda toping.
29) a=2+3i va b=3-2i kompleks sonlar berilgan.
a+b; a-b; a∙b; va a:b sonlarni toping.
30) a=-4-3i va b=4+2i kompleks sonlar berilgan. Bu sonlarning yig’indisi, ayirmasi, ko’paytmasi va bo’linmalarini toping.