(x+2)^2+3(x-1)(x+1)=4x(x-2) eching

$$( x + 2 ) ^ { 2 } + 3 ( x - 1 ) ( x + 1 ) = 4 x ( x - 2 )$$

x uchun yechish

$$x=-\frac{1}{12}\approx -0,083333333$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$x^{2}+4x+4+3\left(x-1\right)\left(x+1\right)=4x\left(x-2\right)$$

3 ga x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}+4x+4+\left(3x-3\right)\left(x+1\right)=4x\left(x-2\right)$$

3x-3 ga x+1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$x^{2}+4x+4+3x^{2}-3=4x\left(x-2\right)$$

4x^{2} ni olish uchun x^{2} va 3x^{2} ni birlashtirish.

$$4x^{2}+4x+4-3=4x\left(x-2\right)$$

1 olish uchun 4 dan 3 ni ayirish.

$$4x^{2}+4x+1=4x\left(x-2\right)$$

4x ga x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4x^{2}+4x+1=4x^{2}-8x$$

Ikkala tarafdan 4x^{2} ni ayirish.

$$4x^{2}+4x+1-4x^{2}=-8x$$

0 ni olish uchun 4x^{2} va -4x^{2} ni birlashtirish.

$$4x+1=-8x$$

8x ni ikki tarafga qo’shing.

$$4x+1+8x=0$$

12x ni olish uchun 4x va 8x ni birlashtirish.

$$12x+1=0$$

Ikkala tarafdan 1 ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$12x=-1$$

Ikki tarafini 12 ga bo‘ling.

$$x=\frac{-1}{12}$$

\frac{-1}{12} kasri manfiy belgini olib tashlash bilan -\frac{1}{12} sifatida qayta yozilishi mumkin.

$$x=-\frac{1}{12}$$