3x(x+1)-(x-2)^2-6=(x+3)(x-5)+x*(x+9)+5 eching

$$3 x ( x + 1 ) - ( x - 2 ) ^ { 2 } - 6 = ( x + 3 ) ( x - 5 ) + x \cdot ( x + 9 ) + 5$$

x uchun yechish (complex solution)

$$x\in \mathrm{C}$$

Yechim qadamlari

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

$$3x^{2}+3x-\left(x-2\right)^{2}-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

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

$$3x^{2}+3x-\left(x^{2}-4x+4\right)-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

x^{2}-4x+4 teskarisini topish uchun har birining teskarisini toping.

$$3x^{2}+3x-x^{2}+4x-4-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

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

$$2x^{2}+3x+4x-4-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

7x ni olish uchun 3x va 4x ni birlashtirish.

$$2x^{2}+7x-4-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

-10 olish uchun -4 dan 6 ni ayirish.

$$2x^{2}+7x-10=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

x+3 ga x-5 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2x^{2}+7x-10=x^{2}-2x-15+x\left(x+9\right)+5$$

x ga x+9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+7x-10=x^{2}-2x-15+x^{2}+9x+5$$

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

$$2x^{2}+7x-10=2x^{2}-2x-15+9x+5$$

7x ni olish uchun -2x va 9x ni birlashtirish.

$$2x^{2}+7x-10=2x^{2}+7x-15+5$$

-10 olish uchun -15 va 5'ni qo'shing.

$$2x^{2}+7x-10=2x^{2}+7x-10$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$2x^{2}+7x-10-2x^{2}=7x-10$$

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

$$7x-10=7x-10$$

Ikkala tarafdan 7x ni ayirish.

$$7x-10-7x=-10$$

0 ni olish uchun 7x va -7x ni birlashtirish.

$$-10=-10$$

-10 va -10 ni taqqoslang.

$$\text{true}$$

Bu har qanday x uchun to‘g‘ri.

$$x\in \mathrm{C}$$

x uchun yechish

$$x\in \mathrm{R}$$

Yechim qadamlari

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

$$3x^{2}+3x-\left(x-2\right)^{2}-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

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

$$3x^{2}+3x-\left(x^{2}-4x+4\right)-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

x^{2}-4x+4 teskarisini topish uchun har birining teskarisini toping.

$$3x^{2}+3x-x^{2}+4x-4-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

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

$$2x^{2}+3x+4x-4-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

7x ni olish uchun 3x va 4x ni birlashtirish.

$$2x^{2}+7x-4-6=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

-10 olish uchun -4 dan 6 ni ayirish.

$$2x^{2}+7x-10=\left(x+3\right)\left(x-5\right)+x\left(x+9\right)+5$$

x+3 ga x-5 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$2x^{2}+7x-10=x^{2}-2x-15+x\left(x+9\right)+5$$

x ga x+9 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}+7x-10=x^{2}-2x-15+x^{2}+9x+5$$

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

$$2x^{2}+7x-10=2x^{2}-2x-15+9x+5$$

7x ni olish uchun -2x va 9x ni birlashtirish.

$$2x^{2}+7x-10=2x^{2}+7x-15+5$$

-10 olish uchun -15 va 5'ni qo'shing.

$$2x^{2}+7x-10=2x^{2}+7x-10$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$2x^{2}+7x-10-2x^{2}=7x-10$$

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

$$7x-10=7x-10$$

Ikkala tarafdan 7x ni ayirish.

$$7x-10-7x=-10$$

0 ni olish uchun 7x va -7x ni birlashtirish.

$$-10=-10$$

-10 va -10 ni taqqoslang.

$$\text{true}$$

Bu har qanday x uchun to‘g‘ri.

$$x\in \mathrm{R}$$