x^2-3x-108? eching

$$x ^ { 2 } - 3 x - 108 ?$$

Omil

$$\left(x-12\right)\left(x+9\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda x^{2}+ax+bx-108 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-3 ab=1\left(-108\right)=-108$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -108-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-108 2,-54 3,-36 4,-27 6,-18 9,-12$$

Har bir juftlik yigʻindisini hisoblang.

$$1-108=-107 2-54=-52 3-36=-33 4-27=-23 6-18=-12 9-12=-3$$

Yechim – -3 yigʻindisini beruvchi juftlik.

$$a=-12 b=9$$

x^{2}-3x-108 ni \left(x^{2}-12x\right)+\left(9x-108\right) sifatida qaytadan yozish.

$$\left(x^{2}-12x\right)+\left(9x-108\right)$$

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

$$x\left(x-12\right)+9\left(x-12\right)$$

Distributiv funktsiyasidan foydalangan holda x-12 umumiy terminini chiqaring.

$$\left(x-12\right)\left(x+9\right)$$

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.

$$x^{2}-3x-108=0$$

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.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-108\right)}}{2}$$

-3 kvadratini chiqarish.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\left(-108\right)}}{2}$$

-4 ni -108 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9+432}}{2}$$

9 ni 432 ga qo'shish.

$$x=\frac{-\left(-3\right)±\sqrt{441}}{2}$$

441 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-3\right)±21}{2}$$

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±21}{2}$$

x=\frac{3±21}{2} tenglamasini yeching, bunda ± musbat. 3 ni 21 ga qo'shish.

$$x=\frac{24}{2}$$

24 ni 2 ga bo'lish.

$$x=12$$

x=\frac{3±21}{2} tenglamasini yeching, bunda ± manfiy. 3 dan 21 ni ayirish.

$$x=-\frac{18}{2}$$

-18 ni 2 ga bo'lish.

$$x=-9$$

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 -9 ga bo‘ling.

$$x^{2}-3x-108=\left(x-12\right)\left(x-\left(-9\right)\right)$$

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

$$x^{2}-3x-108=\left(x-12\right)\left(x+9\right)$$

Baholash

$$\left(x-12\right)\left(x+9\right)$$