11x^2-9x-2 eching

$$11 x ^ { 2 } - 9 x - 2$$

Omil

$$\left(x-1\right)\left(11x+2\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 11x^{2}+ax+bx-2 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-9 ab=11\left(-2\right)=-22$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -22-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-22 2,-11$$

Har bir juftlik yigʻindisini hisoblang.

$$1-22=-21 2-11=-9$$

Yechim – -9 yigʻindisini beruvchi juftlik.

$$a=-11 b=2$$

11x^{2}-9x-2 ni \left(11x^{2}-11x\right)+\left(2x-2\right) sifatida qaytadan yozish.

$$\left(11x^{2}-11x\right)+\left(2x-2\right)$$

Birinchi guruhda 11x ni va ikkinchi guruhda 2 ni faktordan chiqaring.

$$11x\left(x-1\right)+2\left(x-1\right)$$

Distributiv funktsiyasidan foydalangan holda x-1 umumiy terminini chiqaring.

$$\left(x-1\right)\left(11x+2\right)$$

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.

$$11x^{2}-9x-2=0$$

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.

$$x=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 11\left(-2\right)}}{2\times 11}$$

-9 kvadratini chiqarish.

$$x=\frac{-\left(-9\right)±\sqrt{81-4\times 11\left(-2\right)}}{2\times 11}$$

-4 ni 11 marotabaga ko'paytirish.

$$x=\frac{-\left(-9\right)±\sqrt{81-44\left(-2\right)}}{2\times 11}$$

-44 ni -2 marotabaga ko'paytirish.

$$x=\frac{-\left(-9\right)±\sqrt{81+88}}{2\times 11}$$

81 ni 88 ga qo'shish.

$$x=\frac{-\left(-9\right)±\sqrt{169}}{2\times 11}$$

169 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-9\right)±13}{2\times 11}$$

-9 ning teskarisi 9 ga teng.

$$x=\frac{9±13}{2\times 11}$$

2 ni 11 marotabaga ko'paytirish.

$$x=\frac{9±13}{22}$$

x=\frac{9±13}{22} tenglamasini yeching, bunda ± musbat. 9 ni 13 ga qo'shish.

$$x=\frac{22}{22}$$

22 ni 22 ga bo'lish.

$$x=1$$

x=\frac{9±13}{22} tenglamasini yeching, bunda ± manfiy. 9 dan 13 ni ayirish.

$$x=-\frac{4}{22}$$

\frac{-4}{22} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{2}{11}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 1 ga va x_{2} uchun -\frac{2}{11} ga bo‘ling.

$$11x^{2}-9x-2=11\left(x-1\right)\left(x-\left(-\frac{2}{11}\right)\right)$$

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

$$11x^{2}-9x-2=11\left(x-1\right)\left(x+\frac{2}{11}\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{2}{11} ni x ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$11x^{2}-9x-2=11\left(x-1\right)\times \frac{11x+2}{11}$$

11 va 11 ichida eng katta umumiy 11 faktorini bekor qiling.

$$11x^{2}-9x-2=\left(x-1\right)\left(11x+2\right)$$

Baholash

$$\left(x-1\right)\left(11x+2\right)$$