2a^2+a-1 eching

$$2 a ^ { 2 } + a - 1$$

Omil

$$\left(2a-1\right)\left(a+1\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 2a^{2}+pa+qa-1 sifatida qayta yozilishi kerak. p va q ni topish uchun yechiladigan tizimni sozlang.

$$p+q=1 pq=2\left(-1\right)=-2$$

pq manfiy boʻlganda, p va q da qarama-qarshi belgilar bor. p+q musbat boʻlganda, musbat sonda manfiyga nisbatdan kattaroq mutlaq qiymat bor. Faqat bundan juftlik tizim yechimidir.

$$p=-1 q=2$$

2a^{2}+a-1 ni \left(2a^{2}-a\right)+\left(2a-1\right) sifatida qaytadan yozish.

$$\left(2a^{2}-a\right)+\left(2a-1\right)$$

2a^{2}-a ichida a ni ajrating.

$$a\left(2a-1\right)+2a-1$$

Distributiv funktsiyasidan foydalangan holda 2a-1 umumiy terminini chiqaring.

$$\left(2a-1\right)\left(a+1\right)$$

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.

$$2a^{2}+a-1=0$$

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.

$$a=\frac{-1±\sqrt{1^{2}-4\times 2\left(-1\right)}}{2\times 2}$$

1 kvadratini chiqarish.

$$a=\frac{-1±\sqrt{1-4\times 2\left(-1\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$a=\frac{-1±\sqrt{1-8\left(-1\right)}}{2\times 2}$$

-8 ni -1 marotabaga ko'paytirish.

$$a=\frac{-1±\sqrt{1+8}}{2\times 2}$$

1 ni 8 ga qo'shish.

$$a=\frac{-1±\sqrt{9}}{2\times 2}$$

9 ning kvadrat ildizini chiqarish.

$$a=\frac{-1±3}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$a=\frac{-1±3}{4}$$

a=\frac{-1±3}{4} tenglamasini yeching, bunda ± musbat. -1 ni 3 ga qo'shish.

$$a=\frac{2}{4}$$

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

$$a=\frac{1}{2}$$

a=\frac{-1±3}{4} tenglamasini yeching, bunda ± manfiy. -1 dan 3 ni ayirish.

$$a=-\frac{4}{4}$$

-4 ni 4 ga bo'lish.

$$a=-1$$

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

$$2a^{2}+a-1=2\left(a-\frac{1}{2}\right)\left(a-\left(-1\right)\right)$$

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

$$2a^{2}+a-1=2\left(a-\frac{1}{2}\right)\left(a+1\right)$$

Umumiy maxrajni topib va suratlarni ayirib \frac{1}{2} ni a dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

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

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

$$2a^{2}+a-1=\left(2a-1\right)\left(a+1\right)$$

Baholash

$$\left(2a-1\right)\left(a+1\right)$$