z^2+(x+2)z+y(1-2)=0 eching

$${ z }^{ 2 } +(x+2)z+y(1-2)=0$$

x uchun yechish

$$\left\{\begin{matrix}x=-z+\frac{y}{z}-2\text{, }&z\neq 0\\x\in \mathrm{R}\text{, }&y=0\text{ and }z=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x+2 ga z ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$z^{2}+xz+2z+y\left(1-2\right)=0$$

-1 olish uchun 1 dan 2 ni ayirish.

$$z^{2}+xz+2z+y\left(-1\right)=0$$

Ikkala tarafdan z^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$xz+2z+y\left(-1\right)=-z^{2}$$

Ikkala tarafdan 2z ni ayirish.

$$xz+y\left(-1\right)=-z^{2}-2z$$

Ikkala tarafdan y\left(-1\right) ni ayirish.

$$xz=-z^{2}-2z-y\left(-1\right)$$

1 hosil qilish uchun -1 va -1 ni ko'paytirish.

$$xz=-z^{2}-2z+y$$

Tenglama standart shaklda.

$$zx=y-z^{2}-2z$$

Ikki tarafini z ga bo‘ling.

$$\frac{zx}{z}=\frac{y-z^{2}-2z}{z}$$

z ga bo'lish z ga ko'paytirishni bekor qiladi.

$$x=\frac{y-z^{2}-2z}{z}$$

-z^{2}-2z+y ni z ga bo'lish.

$$x=-z+\frac{y}{z}-2$$

y uchun yechish

$$y=z\left(x+z+2\right)$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x+2 ga z ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$z^{2}+xz+2z+y\left(1-2\right)=0$$

-1 olish uchun 1 dan 2 ni ayirish.

$$z^{2}+xz+2z+y\left(-1\right)=0$$

Ikkala tarafdan z^{2} ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

$$xz+2z+y\left(-1\right)=-z^{2}$$

Ikkala tarafdan xz ni ayirish.

$$2z+y\left(-1\right)=-z^{2}-xz$$

Ikkala tarafdan 2z ni ayirish.

$$y\left(-1\right)=-z^{2}-xz-2z$$

Tenglama standart shaklda.

$$-y=-xz-z^{2}-2z$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-y}{-1}=-\frac{z\left(x+z+2\right)}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$y=-\frac{z\left(x+z+2\right)}{-1}$$

-z\left(2+z+x\right) ni -1 ga bo'lish.

$$y=z\left(x+z+2\right)$$