$a$ va $b$ raqamlarni toping, agar $\overline{a13b}$ soni 72 ga bo'linsa.
- A. a = 8, b = 5
- B. a = 6, b = 8
- C. a = 8, b = 6
- D. a = 7, b = 6
Bo'linish belgilari, tub va murakkab sonlar bo‘yicha savol
Javob va yechimni ko‘rish
Javob: a = 8, b = 6
$\overline{a13b}=1000a+130+ b$.
72 ga bo‘linishi uchun $ \overline{a13b}\equiv0\pmod 8$ va $ \overline{a13b}\equiv0\pmod 9$ bo‘lishi kerak (72 = $8\cdot9$).
*Modul 8:* $1000a\equiv0$, $130\equiv2$, shuning uchun $2+b\equiv0\pmod8\Rightarrow b\equiv6\pmod8$. Demak $b=6$ (raqam $0\le b\le9$).
*Modul 9:* $1000a\equiv a$, $130\equiv4$, shuning uchun $a+4+ b\equiv0\pmod9$. $b=6$ qo‘yib, $a+10\equiv0\pmod9\Rightarrow a\equiv8\pmod9$, ya’ni $a=8$.
Shu bilan $a=8$, $b=6$ va bu A variantiga mos keladi.
Mavzuni mustahkamlang
Bu savol Bo'linish belgilari, tub va murakkab sonlar mavzusiga tegishli. Ta’riflar, formulalar va misollarni mavzu sahifasida ko‘ring.
Mavzuni o‘rganish