(3x+1)^2=3(3x^2+x-2) eching

$$( 3 x + 1 ) ^ { 2 } = 3 ( 3 x ^ { 2 } + x - 2 )$$

x uchun yechish

$$x = -\frac{7}{3} = -2\frac{1}{3} \approx -2,333333333$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(3x+1\right)^{2} kengaytirilishi uchun ishlating.

$$9x^{2}+6x+1=3\left(3x^{2}+x-2\right)$$

3 ga 3x^{2}+x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$9x^{2}+6x+1=9x^{2}+3x-6$$

Ikkala tarafdan 9x^{2} ni ayirish.

$$9x^{2}+6x+1-9x^{2}=3x-6$$

0 ni olish uchun 9x^{2} va -9x^{2} ni birlashtirish.

$$6x+1=3x-6$$

Ikkala tarafdan 3x ni ayirish.

$$6x+1-3x=-6$$

3x ni olish uchun 6x va -3x ni birlashtirish.

$$3x+1=-6$$

Ikkala tarafdan 1 ni ayirish.

$$3x=-6-1$$

-7 olish uchun -6 dan 1 ni ayirish.

$$3x=-7$$

Ikki tarafini 3 ga bo‘ling.

$$x=\frac{-7}{3}$$

\frac{-7}{3} kasri manfiy belgini olib tashlash bilan -\frac{7}{3} sifatida qayta yozilishi mumkin.

$$x=-\frac{7}{3}$$