2x^2+3x+1 eching

$$2 x ^ { 2 } + 3 x + 1$$

Omil

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

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 2x^{2}+ax+bx+1 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=3 ab=2\times 1=2$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b musbat boʻlganda, a va b ikkisi ham musbat. Faqat bundan juftlik tizim yechimidir.

$$a=1 b=2$$

2x^{2}+3x+1 ni \left(2x^{2}+x\right)+\left(2x+1\right) sifatida qaytadan yozish.

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

2x^{2}+x ichida x ni ajrating.

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

Distributiv funktsiyasidan foydalangan holda 2x+1 umumiy terminini chiqaring.

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

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.

$$2x^{2}+3x+1=0$$

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.

$$x=\frac{-3±\sqrt{3^{2}-4\times 2}}{2\times 2}$$

3 kvadratini chiqarish.

$$x=\frac{-3±\sqrt{9-4\times 2}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{9-8}}{2\times 2}$$

9 ni -8 ga qo'shish.

$$x=\frac{-3±\sqrt{1}}{2\times 2}$$

1 ning kvadrat ildizini chiqarish.

$$x=\frac{-3±1}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{-3±1}{4}$$

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

$$x=-\frac{2}{4}$$

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

$$x=-\frac{1}{2}$$

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

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

-4 ni 4 ga bo'lish.

$$x=-1$$

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.

$$2x^{2}+3x+1=2\left(x-\left(-\frac{1}{2}\right)\right)\left(x-\left(-1\right)\right)$$

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

$$2x^{2}+3x+1=2\left(x+\frac{1}{2}\right)\left(x+1\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{2} ni x ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$2x^{2}+3x+1=2\times \frac{2x+1}{2}\left(x+1\right)$$

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

$$2x^{2}+3x+1=\left(2x+1\right)\left(x+1\right)$$

Baholash

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