2n^2+28n+96 eching

$$2 n ^ { 2 } + 28 n + 96$$

Omil

$$2\left(n+6\right)\left(n+8\right)$$

Yechim qadamlari

2 omili.

$$2\left(n^{2}+14n+48\right)$$

Hisoblang: n^{2}+14n+48. Ifodani guruhlash orqali faktorlang. Avvalo, ifoda n^{2}+an+bn+48 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=14 ab=1\times 48=48$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b musbat boʻlganda, a va b ikkisi ham musbat. 48-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,48 2,24 3,16 4,12 6,8$$

Har bir juftlik yigʻindisini hisoblang.

$$1+48=49 2+24=26 3+16=19 4+12=16 6+8=14$$

Yechim – 14 yigʻindisini beruvchi juftlik.

$$a=6 b=8$$

n^{2}+14n+48 ni \left(n^{2}+6n\right)+\left(8n+48\right) sifatida qaytadan yozish.

$$\left(n^{2}+6n\right)+\left(8n+48\right)$$

Birinchi guruhda n ni va ikkinchi guruhda 8 ni faktordan chiqaring.

$$n\left(n+6\right)+8\left(n+6\right)$$

Distributiv funktsiyasidan foydalangan holda n+6 umumiy terminini chiqaring.

$$\left(n+6\right)\left(n+8\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$2\left(n+6\right)\left(n+8\right)$$

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.

$$2n^{2}+28n+96=0$$

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.

$$n=\frac{-28±\sqrt{28^{2}-4\times 2\times 96}}{2\times 2}$$

28 kvadratini chiqarish.

$$n=\frac{-28±\sqrt{784-4\times 2\times 96}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$n=\frac{-28±\sqrt{784-8\times 96}}{2\times 2}$$

-8 ni 96 marotabaga ko'paytirish.

$$n=\frac{-28±\sqrt{784-768}}{2\times 2}$$

784 ni -768 ga qo'shish.

$$n=\frac{-28±\sqrt{16}}{2\times 2}$$

16 ning kvadrat ildizini chiqarish.

$$n=\frac{-28±4}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$n=\frac{-28±4}{4}$$

n=\frac{-28±4}{4} tenglamasini yeching, bunda ± musbat. -28 ni 4 ga qo'shish.

$$n=-\frac{24}{4}$$

-24 ni 4 ga bo'lish.

$$n=-6$$

n=\frac{-28±4}{4} tenglamasini yeching, bunda ± manfiy. -28 dan 4 ni ayirish.

$$n=-\frac{32}{4}$$

-32 ni 4 ga bo'lish.

$$n=-8$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -6 ga va x_{2} uchun -8 ga bo‘ling.

$$2n^{2}+28n+96=2\left(n-\left(-6\right)\right)\left(n-\left(-8\right)\right)$$

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

$$2n^{2}+28n+96=2\left(n+6\right)\left(n+8\right)$$

Baholash

$$2\left(n+6\right)\left(n+8\right)$$