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

7. “Tub va murakkab sonlar. Ikki yoki bir necha sonlarning EKUB va EKUK larni topish” mavzusiga doir topshiriqlar.
1) Quyidagi sonlardan qaysilari tub son. Javobingizni izohlang.

253; 563; 863 va 977

2) Quyidagi sonlardan qaysilari tub son. Javobingizni izohlang.

367; 581; 847 va 1003

3) Quyidagi sonlardan qaysilari tub son. Javobingizni izohlang.

1923; 567; 983 va 487

4) Quyidagi sonlardan qaysilari tub son. Javobingizni izohlang.

923; 557; 347; va 881

5) 900 sonining nechta bo’luvchisi bor. Ularni yozing.

6) 1280 sonining nechta bo’luvchisi bor. Ularni yozing.

7) 720 sonining nechta bo’luvchisi bor. Ularni yozing.

8) 800 sonining nechta bo’luvchisi bor. Ularni yozing.

9) Quyidagi sonlarning EKUB va EKUK ni toping.

(320; 560) va (196; 224)

10) Quyidagi sonlarning EKUB va EKUK ni toping.

(588; 2058) va (284; 372)

11) Quyidagi sonlarning EKUB va EKUK ni toping.

(548; 386) va (840; 564)

12) Quyidagi sonlarning EKUB va EKUK ni toping.

(1124; 296) va (388; 522)

13) Agar ikki sonning EKUBi 28 teng bo’lib, bu sonlar 5:9 kabi munosabatda bo’lsa, bu sonlarni toping.

14) Agar ikki sonning EKUKi 3960 teng bo’lib, bu sonlar 11:30 kabi munosabatda bo’lsa, bu sonlarni toping.

15) 320 ta yong’oq, 240 ta olma va 240 ta konfet bor. Bu narsalarni teng taqsimlab ko’pi bilan nechta sovg’a tayyorlash mumkin?

16) EKUBi 24 ga, Ekuki 2496 ga teng bo’lgan sonlarni toping.

17) Yevklid algoritmidan foydalanib quyidagi sonlarning EKUB ni toping.

324 va 1644; 928 va 1364;

18) Yevklid algoritmidan foydalanib quyidagi sonlarning EKUB ni toping.

1540 va 860; 344 va 768;

19) Yevklid algoritmidan foydalanib quyidagi sonlarning EKUB ni toping.

866 va 448; 1328 va 324;

20) Yevklid algoritmidan foydalanib quyidagi sonlarning EKUB ni toping.

962 va 364; 1566 va 584;

21) “997, 797, 397, 297 sonlar tub sonlardir” degan mulohazani isbotlang yoki rad eting.

22) “661, 1261, 853, 337 sonlaridan hech bo’lmasa birtasi murakkab” mulohazani isbotlang yoki rad eting.

23) Sonlarni tub ko’paytuvchilarga ajrating va ularning EKUBini toping.

2742 va 15060; 3644 va 8642

24) Sonlarni tub ko’paytuvchilarga ajrating va ularning EKUBini toping.

3640 va 2820; 2462 va 1744

25) Sonlarni tub ko’paytuvchilarga ajrating va ularning EKUBini toping.

1864 va 3228; 1460 va 866

26) Sonlarni tub ko’paytuvchilarga ajrating va ularning EKUBini toping.

960 va 2324; 888 va 1222

27) Ikki sonning ko’paytmasi 67392 ga teng. Ularning EKUBi 24 ga teng. Shu sonlarning EKUK ni toping.

28) Ikki sonning ko’paytmasi 84320 ga teng. Ularning EKUBi 4 ga teng. Shu sonlarning EKUK ni toping.

29) Yevklid algoritmidan foydalanib, EKUB ini toping.

a)1995 va 1280; b) 2263 va 8249

30) Yevklid algoritmidan foydalanib, EKUB ini toping.

a) 45469 va 41033; b) 17593 va 9660

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.