6w^2+55w+9 eching

$$6 w ^ { 2 } + 55 w + 9$$

Omil

$$\left(w+9\right)\left(6w+1\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 6w^{2}+aw+bw+9 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=55 ab=6\times 9=54$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b musbat boʻlganda, a va b ikkisi ham musbat. 54-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,54 2,27 3,18 6,9$$

Har bir juftlik yigʻindisini hisoblang.

$$1+54=55 2+27=29 3+18=21 6+9=15$$

Yechim – 55 yigʻindisini beruvchi juftlik.

$$a=1 b=54$$

6w^{2}+55w+9 ni \left(6w^{2}+w\right)+\left(54w+9\right) sifatida qaytadan yozish.

$$\left(6w^{2}+w\right)+\left(54w+9\right)$$

Birinchi guruhda w ni va ikkinchi guruhda 9 ni faktordan chiqaring.

$$w\left(6w+1\right)+9\left(6w+1\right)$$

Distributiv funktsiyasidan foydalangan holda 6w+1 umumiy terminini chiqaring.

$$\left(6w+1\right)\left(w+9\right)$$

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.

$$6w^{2}+55w+9=0$$

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.

$$w=\frac{-55±\sqrt{55^{2}-4\times 6\times 9}}{2\times 6}$$

55 kvadratini chiqarish.

$$w=\frac{-55±\sqrt{3025-4\times 6\times 9}}{2\times 6}$$

-4 ni 6 marotabaga ko'paytirish.

$$w=\frac{-55±\sqrt{3025-24\times 9}}{2\times 6}$$

-24 ni 9 marotabaga ko'paytirish.

$$w=\frac{-55±\sqrt{3025-216}}{2\times 6}$$

3025 ni -216 ga qo'shish.

$$w=\frac{-55±\sqrt{2809}}{2\times 6}$$

2809 ning kvadrat ildizini chiqarish.

$$w=\frac{-55±53}{2\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$w=\frac{-55±53}{12}$$

w=\frac{-55±53}{12} tenglamasini yeching, bunda ± musbat. -55 ni 53 ga qo'shish.

$$w=-\frac{2}{12}$$

\frac{-2}{12} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$w=-\frac{1}{6}$$

w=\frac{-55±53}{12} tenglamasini yeching, bunda ± manfiy. -55 dan 53 ni ayirish.

$$w=-\frac{108}{12}$$

-108 ni 12 ga bo'lish.

$$w=-9$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -\frac{1}{6} ga va x_{2} uchun -9 ga bo‘ling.

$$6w^{2}+55w+9=6\left(w-\left(-\frac{1}{6}\right)\right)\left(w-\left(-9\right)\right)$$

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

$$6w^{2}+55w+9=6\left(w+\frac{1}{6}\right)\left(w+9\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{6} ni w ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$6w^{2}+55w+9=6\times \frac{6w+1}{6}\left(w+9\right)$$

6 va 6 ichida eng katta umumiy 6 faktorini bekor qiling.

$$6w^{2}+55w+9=\left(6w+1\right)\left(w+9\right)$$

Baholash

$$\left(w+9\right)\left(6w+1\right)$$