8b^2-2b-3 eching

$$8 b ^ { 2 } - 2 b - 3$$

Omil

$$\left(4b-3\right)\left(2b+1\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 8b^{2}+pb+qb-3 sifatida qayta yozilishi kerak. p va q ni topish uchun yechiladigan tizimni sozlang.

$$p+q=-2 pq=8\left(-3\right)=-24$$

pq manfiy boʻlganda, p va q da qarama-qarshi belgilar bor. p+q manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -24-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-24 2,-12 3,-8 4,-6$$

Har bir juftlik yigʻindisini hisoblang.

$$1-24=-23 2-12=-10 3-8=-5 4-6=-2$$

Yechim – -2 yigʻindisini beruvchi juftlik.

$$p=-6 q=4$$

8b^{2}-2b-3 ni \left(8b^{2}-6b\right)+\left(4b-3\right) sifatida qaytadan yozish.

$$\left(8b^{2}-6b\right)+\left(4b-3\right)$$

8b^{2}-6b ichida 2b ni ajrating.

$$2b\left(4b-3\right)+4b-3$$

Distributiv funktsiyasidan foydalangan holda 4b-3 umumiy terminini chiqaring.

$$\left(4b-3\right)\left(2b+1\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

Kvadrat koʻp tenglama bu orqali hisoblanadi: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), bu yerda x_{1} va x_{2} ax^{2}+bx+c=0 kvadrat tenglamaning yechimlari.

$$8b^{2}-2b-3=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$b=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 8\left(-3\right)}}{2\times 8}$$

-2 kvadratini chiqarish.

$$b=\frac{-\left(-2\right)±\sqrt{4-4\times 8\left(-3\right)}}{2\times 8}$$

-4 ni 8 marotabaga ko'paytirish.

$$b=\frac{-\left(-2\right)±\sqrt{4-32\left(-3\right)}}{2\times 8}$$

-32 ni -3 marotabaga ko'paytirish.

$$b=\frac{-\left(-2\right)±\sqrt{4+96}}{2\times 8}$$

4 ni 96 ga qo'shish.

$$b=\frac{-\left(-2\right)±\sqrt{100}}{2\times 8}$$

100 ning kvadrat ildizini chiqarish.

$$b=\frac{-\left(-2\right)±10}{2\times 8}$$

-2 ning teskarisi 2 ga teng.

$$b=\frac{2±10}{2\times 8}$$

2 ni 8 marotabaga ko'paytirish.

$$b=\frac{2±10}{16}$$

b=\frac{2±10}{16} tenglamasini yeching, bunda ± musbat. 2 ni 10 ga qo'shish.

$$b=\frac{12}{16}$$

\frac{12}{16} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$b=\frac{3}{4}$$

b=\frac{2±10}{16} tenglamasini yeching, bunda ± manfiy. 2 dan 10 ni ayirish.

$$b=-\frac{8}{16}$$

\frac{-8}{16} ulushini 8 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$b=-\frac{1}{2}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{3}{4} ga va x_{2} uchun -\frac{1}{2} ga bo‘ling.

$$8b^{2}-2b-3=8\left(b-\frac{3}{4}\right)\left(b-\left(-\frac{1}{2}\right)\right)$$

p-\left(-q\right) shaklining barcha amallarigani p+q ga soddalashtiring.

$$8b^{2}-2b-3=8\left(b-\frac{3}{4}\right)\left(b+\frac{1}{2}\right)$$

Umumiy maxrajni topib va suratlarni ayirib \frac{3}{4} ni b dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$8b^{2}-2b-3=8\times \frac{4b-3}{4}\left(b+\frac{1}{2}\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{2} ni b ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$8b^{2}-2b-3=8\times \frac{4b-3}{4}\times \frac{2b+1}{2}$$

Raqamlash sonlarini va maxraj sonlariga ko'paytirish orqali \frac{4b-3}{4} ni \frac{2b+1}{2} ga ko'paytirish. So'ngra kasrni imkoni boricha eng kam a'zoga qisqartiring.

$$8b^{2}-2b-3=8\times \frac{\left(4b-3\right)\left(2b+1\right)}{4\times 2}$$

4 ni 2 marotabaga ko'paytirish.

$$8b^{2}-2b-3=8\times \frac{\left(4b-3\right)\left(2b+1\right)}{8}$$

8 va 8 ichida eng katta umumiy 8 faktorini bekor qiling.

$$8b^{2}-2b-3=\left(4b-3\right)\left(2b+1\right)$$

Baholash

$$\left(4b-3\right)\left(2b+1\right)$$