9y^2-104y-48 eching

$$9 y ^ { 2 } - 104 y - 48$$

Omil

$$\left(y-12\right)\left(9y+4\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 9y^{2}+ay+by-48 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-104 ab=9\left(-48\right)=-432$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -432-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-432 2,-216 3,-144 4,-108 6,-72 8,-54 9,-48 12,-36 16,-27 18,-24$$

Har bir juftlik yigʻindisini hisoblang.

$$1-432=-431 2-216=-214 3-144=-141 4-108=-104 6-72=-66 8-54=-46 9-48=-39 12-36=-24 16-27=-11 18-24=-6$$

Yechim – -104 yigʻindisini beruvchi juftlik.

$$a=-108 b=4$$

9y^{2}-104y-48 ni \left(9y^{2}-108y\right)+\left(4y-48\right) sifatida qaytadan yozish.

$$\left(9y^{2}-108y\right)+\left(4y-48\right)$$

Birinchi guruhda 9y ni va ikkinchi guruhda 4 ni faktordan chiqaring.

$$9y\left(y-12\right)+4\left(y-12\right)$$

Distributiv funktsiyasidan foydalangan holda y-12 umumiy terminini chiqaring.

$$\left(y-12\right)\left(9y+4\right)$$

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.

$$9y^{2}-104y-48=0$$

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.

$$y=\frac{-\left(-104\right)±\sqrt{\left(-104\right)^{2}-4\times 9\left(-48\right)}}{2\times 9}$$

-104 kvadratini chiqarish.

$$y=\frac{-\left(-104\right)±\sqrt{10816-4\times 9\left(-48\right)}}{2\times 9}$$

-4 ni 9 marotabaga ko'paytirish.

$$y=\frac{-\left(-104\right)±\sqrt{10816-36\left(-48\right)}}{2\times 9}$$

-36 ni -48 marotabaga ko'paytirish.

$$y=\frac{-\left(-104\right)±\sqrt{10816+1728}}{2\times 9}$$

10816 ni 1728 ga qo'shish.

$$y=\frac{-\left(-104\right)±\sqrt{12544}}{2\times 9}$$

12544 ning kvadrat ildizini chiqarish.

$$y=\frac{-\left(-104\right)±112}{2\times 9}$$

-104 ning teskarisi 104 ga teng.

$$y=\frac{104±112}{2\times 9}$$

2 ni 9 marotabaga ko'paytirish.

$$y=\frac{104±112}{18}$$

y=\frac{104±112}{18} tenglamasini yeching, bunda ± musbat. 104 ni 112 ga qo'shish.

$$y=\frac{216}{18}$$

216 ni 18 ga bo'lish.

$$y=12$$

y=\frac{104±112}{18} tenglamasini yeching, bunda ± manfiy. 104 dan 112 ni ayirish.

$$y=-\frac{8}{18}$$

\frac{-8}{18} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$y=-\frac{4}{9}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 12 ga va x_{2} uchun -\frac{4}{9} ga bo‘ling.

$$9y^{2}-104y-48=9\left(y-12\right)\left(y-\left(-\frac{4}{9}\right)\right)$$

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

$$9y^{2}-104y-48=9\left(y-12\right)\left(y+\frac{4}{9}\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{4}{9} ni y ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$9y^{2}-104y-48=9\left(y-12\right)\times \frac{9y+4}{9}$$

9 va 9 ichida eng katta umumiy 9 faktorini bekor qiling.

$$9y^{2}-104y-48=\left(y-12\right)\left(9y+4\right)$$

Baholash

$$\left(y-12\right)\left(9y+4\right)$$