2s^2+9s+9 eching

$$2 s ^ { 2 } + 9 s + 9$$

Omil

$$\left(s+3\right)\left(2s+3\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 2s^{2}+as+bs+9 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=9 ab=2\times 9=18$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b musbat boʻlganda, a va b ikkisi ham musbat. 18-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

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

Har bir juftlik yigʻindisini hisoblang.

$$1+18=19 2+9=11 3+6=9$$

Yechim – 9 yigʻindisini beruvchi juftlik.

$$a=3 b=6$$

2s^{2}+9s+9 ni \left(2s^{2}+3s\right)+\left(6s+9\right) sifatida qaytadan yozish.

$$\left(2s^{2}+3s\right)+\left(6s+9\right)$$

Birinchi guruhda s ni va ikkinchi guruhda 3 ni faktordan chiqaring.

$$s\left(2s+3\right)+3\left(2s+3\right)$$

Distributiv funktsiyasidan foydalangan holda 2s+3 umumiy terminini chiqaring.

$$\left(2s+3\right)\left(s+3\right)$$

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.

$$2s^{2}+9s+9=0$$

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.

$$s=\frac{-9±\sqrt{9^{2}-4\times 2\times 9}}{2\times 2}$$

9 kvadratini chiqarish.

$$s=\frac{-9±\sqrt{81-4\times 2\times 9}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$s=\frac{-9±\sqrt{81-8\times 9}}{2\times 2}$$

-8 ni 9 marotabaga ko'paytirish.

$$s=\frac{-9±\sqrt{81-72}}{2\times 2}$$

81 ni -72 ga qo'shish.

$$s=\frac{-9±\sqrt{9}}{2\times 2}$$

9 ning kvadrat ildizini chiqarish.

$$s=\frac{-9±3}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$s=\frac{-9±3}{4}$$

s=\frac{-9±3}{4} tenglamasini yeching, bunda ± musbat. -9 ni 3 ga qo'shish.

$$s=-\frac{6}{4}$$

\frac{-6}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$s=-\frac{3}{2}$$

s=\frac{-9±3}{4} tenglamasini yeching, bunda ± manfiy. -9 dan 3 ni ayirish.

$$s=-\frac{12}{4}$$

-12 ni 4 ga bo'lish.

$$s=-3$$

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

$$2s^{2}+9s+9=2\left(s-\left(-\frac{3}{2}\right)\right)\left(s-\left(-3\right)\right)$$

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

$$2s^{2}+9s+9=2\left(s+\frac{3}{2}\right)\left(s+3\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{3}{2} ni s ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$2s^{2}+9s+9=2\times \frac{2s+3}{2}\left(s+3\right)$$

2 va 2 ichida eng katta umumiy 2 faktorini bekor qiling.

$$2s^{2}+9s+9=\left(2s+3\right)\left(s+3\right)$$

Baholash

$$\left(s+3\right)\left(2s+3\right)$$