a^2+33a+252 eching

$$a ^ { 2 } + 33 a + 252$$

Omil

$$\left(a+12\right)\left(a+21\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda a^{2}+pa+qa+252 sifatida qayta yozilishi kerak. p va q ni topish uchun yechiladigan tizimni sozlang.

$$p+q=33 pq=1\times 252=252$$

pq musbat boʻlganda, p va q da bir xil belgi bor. p+q musbat boʻlganda, p va q ikkisi ham musbat. 252-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,252 2,126 3,84 4,63 6,42 7,36 9,28 12,21 14,18$$

Har bir juftlik yigʻindisini hisoblang.

$$1+252=253 2+126=128 3+84=87 4+63=67 6+42=48 7+36=43 9+28=37 12+21=33 14+18=32$$

Yechim – 33 yigʻindisini beruvchi juftlik.

$$p=12 q=21$$

a^{2}+33a+252 ni \left(a^{2}+12a\right)+\left(21a+252\right) sifatida qaytadan yozish.

$$\left(a^{2}+12a\right)+\left(21a+252\right)$$

Birinchi guruhda a ni va ikkinchi guruhda 21 ni faktordan chiqaring.

$$a\left(a+12\right)+21\left(a+12\right)$$

Distributiv funktsiyasidan foydalangan holda a+12 umumiy terminini chiqaring.

$$\left(a+12\right)\left(a+21\right)$$

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.

$$a^{2}+33a+252=0$$

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.

$$a=\frac{-33±\sqrt{33^{2}-4\times 252}}{2}$$

33 kvadratini chiqarish.

$$a=\frac{-33±\sqrt{1089-4\times 252}}{2}$$

-4 ni 252 marotabaga ko'paytirish.

$$a=\frac{-33±\sqrt{1089-1008}}{2}$$

1089 ni -1008 ga qo'shish.

$$a=\frac{-33±\sqrt{81}}{2}$$

81 ning kvadrat ildizini chiqarish.

$$a=\frac{-33±9}{2}$$

a=\frac{-33±9}{2} tenglamasini yeching, bunda ± musbat. -33 ni 9 ga qo'shish.

$$a=-\frac{24}{2}$$

-24 ni 2 ga bo'lish.

$$a=-12$$

a=\frac{-33±9}{2} tenglamasini yeching, bunda ± manfiy. -33 dan 9 ni ayirish.

$$a=-\frac{42}{2}$$

-42 ni 2 ga bo'lish.

$$a=-21$$

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 -21 ga bo‘ling.

$$a^{2}+33a+252=\left(a-\left(-12\right)\right)\left(a-\left(-21\right)\right)$$

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

$$a^{2}+33a+252=\left(a+12\right)\left(a+21\right)$$

Baholash

$$\left(a+12\right)\left(a+21\right)$$