56x^2-9x-2 eching

$$56 x ^ { 2 } - 9 x - 2$$

Omil

$$\left(7x-2\right)\left(8x+1\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 56x^{2}+ax+bx-2 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-9 ab=56\left(-2\right)=-112$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -112-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-112 2,-56 4,-28 7,-16 8,-14$$

Har bir juftlik yigʻindisini hisoblang.

$$1-112=-111 2-56=-54 4-28=-24 7-16=-9 8-14=-6$$

Yechim – -9 yigʻindisini beruvchi juftlik.

$$a=-16 b=7$$

56x^{2}-9x-2 ni \left(56x^{2}-16x\right)+\left(7x-2\right) sifatida qaytadan yozish.

$$\left(56x^{2}-16x\right)+\left(7x-2\right)$$

56x^{2}-16x ichida 8x ni ajrating.

$$8x\left(7x-2\right)+7x-2$$

Distributiv funktsiyasidan foydalangan holda 7x-2 umumiy terminini chiqaring.

$$\left(7x-2\right)\left(8x+1\right)$$

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.

$$56x^{2}-9x-2=0$$

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.

$$x=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 56\left(-2\right)}}{2\times 56}$$

-9 kvadratini chiqarish.

$$x=\frac{-\left(-9\right)±\sqrt{81-4\times 56\left(-2\right)}}{2\times 56}$$

-4 ni 56 marotabaga ko'paytirish.

$$x=\frac{-\left(-9\right)±\sqrt{81-224\left(-2\right)}}{2\times 56}$$

-224 ni -2 marotabaga ko'paytirish.

$$x=\frac{-\left(-9\right)±\sqrt{81+448}}{2\times 56}$$

81 ni 448 ga qo'shish.

$$x=\frac{-\left(-9\right)±\sqrt{529}}{2\times 56}$$

529 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-9\right)±23}{2\times 56}$$

-9 ning teskarisi 9 ga teng.

$$x=\frac{9±23}{2\times 56}$$

2 ni 56 marotabaga ko'paytirish.

$$x=\frac{9±23}{112}$$

x=\frac{9±23}{112} tenglamasini yeching, bunda ± musbat. 9 ni 23 ga qo'shish.

$$x=\frac{32}{112}$$

\frac{32}{112} ulushini 16 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{2}{7}$$

x=\frac{9±23}{112} tenglamasini yeching, bunda ± manfiy. 9 dan 23 ni ayirish.

$$x=-\frac{14}{112}$$

\frac{-14}{112} ulushini 14 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{1}{8}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{2}{7} ga va x_{2} uchun -\frac{1}{8} ga bo‘ling.

$$56x^{2}-9x-2=56\left(x-\frac{2}{7}\right)\left(x-\left(-\frac{1}{8}\right)\right)$$

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

$$56x^{2}-9x-2=56\left(x-\frac{2}{7}\right)\left(x+\frac{1}{8}\right)$$

Umumiy maxrajni topib va suratlarni ayirib \frac{2}{7} ni x dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$56x^{2}-9x-2=56\times \frac{7x-2}{7}\left(x+\frac{1}{8}\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{8} ni x ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$56x^{2}-9x-2=56\times \frac{7x-2}{7}\times \frac{8x+1}{8}$$

Raqamlash sonlarini va maxraj sonlariga ko'paytirish orqali \frac{7x-2}{7} ni \frac{8x+1}{8} ga ko'paytirish. So'ngra kasrni imkoni boricha eng kam a'zoga qisqartiring.

$$56x^{2}-9x-2=56\times \frac{\left(7x-2\right)\left(8x+1\right)}{7\times 8}$$

7 ni 8 marotabaga ko'paytirish.

$$56x^{2}-9x-2=56\times \frac{\left(7x-2\right)\left(8x+1\right)}{56}$$

56 va 56 ichida eng katta umumiy 56 faktorini bekor qiling.

$$56x^{2}-9x-2=\left(7x-2\right)\left(8x+1\right)$$

Baholash

$$\left(7x-2\right)\left(8x+1\right)$$