x(x-a)+y(y-c)=0 eching

$$x ( x - a ) + y ( y - c ) = 0$$

a uchun yechish (complex solution)

$$\left\{\begin{matrix}a=\frac{x^{2}+y^{2}-cy}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&\left(y=0\text{ or }y=c\right)\text{ and }x=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$x^{2}-xa+y\left(y-c\right)=0$$

y ga y-c ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}-xa+y^{2}-yc=0$$

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

$$-xa+y^{2}-yc=-x^{2}$$

Ikkala tarafdan y^{2} ni ayirish.

$$-xa-yc=-x^{2}-y^{2}$$

yc ni ikki tarafga qo’shing.

$$-xa=-x^{2}-y^{2}+yc$$

Tenglama standart shaklda.

$$\left(-x\right)a=cy-y^{2}-x^{2}$$

Ikki tarafini -x ga bo‘ling.

$$\frac{\left(-x\right)a}{-x}=\frac{cy-y^{2}-x^{2}}{-x}$$

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

$$a=\frac{cy-y^{2}-x^{2}}{-x}$$

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

$$a=\frac{y^{2}-cy}{x}+x$$

c uchun yechish (complex solution)

$$\left\{\begin{matrix}c=\frac{x^{2}-ax+y^{2}}{y}\text{, }&y\neq 0\\c\in \mathrm{C}\text{, }&\left(x=0\text{ or }x=a\right)\text{ and }y=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$x^{2}-xa+y\left(y-c\right)=0$$

y ga y-c ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}-xa+y^{2}-yc=0$$

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

$$-xa+y^{2}-yc=-x^{2}$$

xa ni ikki tarafga qo’shing.

$$y^{2}-yc=-x^{2}+xa$$

Ikkala tarafdan y^{2} ni ayirish.

$$-yc=-x^{2}+xa-y^{2}$$

Tenglama standart shaklda.

$$\left(-y\right)c=ax-y^{2}-x^{2}$$

Ikki tarafini -y ga bo‘ling.

$$\frac{\left(-y\right)c}{-y}=\frac{ax-y^{2}-x^{2}}{-y}$$

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

$$c=\frac{ax-y^{2}-x^{2}}{-y}$$

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

$$c=\frac{x^{2}-ax}{y}+y$$

a uchun yechish

$$\left\{\begin{matrix}a=\frac{x^{2}+y^{2}-cy}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&\left(y=0\text{ or }y=c\right)\text{ and }x=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$x^{2}-xa+y\left(y-c\right)=0$$

y ga y-c ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}-xa+y^{2}-yc=0$$

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

$$-xa+y^{2}-yc=-x^{2}$$

Ikkala tarafdan y^{2} ni ayirish.

$$-xa-yc=-x^{2}-y^{2}$$

yc ni ikki tarafga qo’shing.

$$-xa=-x^{2}-y^{2}+yc$$

Tenglama standart shaklda.

$$\left(-x\right)a=cy-y^{2}-x^{2}$$

Ikki tarafini -x ga bo‘ling.

$$\frac{\left(-x\right)a}{-x}=\frac{cy-y^{2}-x^{2}}{-x}$$

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

$$a=\frac{cy-y^{2}-x^{2}}{-x}$$

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

$$a=\frac{y^{2}-cy}{x}+x$$

c uchun yechish

$$\left\{\begin{matrix}c=\frac{x^{2}-ax+y^{2}}{y}\text{, }&y\neq 0\\c\in \mathrm{R}\text{, }&\left(x=0\text{ or }x=a\right)\text{ and }y=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$x^{2}-xa+y\left(y-c\right)=0$$

y ga y-c ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}-xa+y^{2}-yc=0$$

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

$$-xa+y^{2}-yc=-x^{2}$$

xa ni ikki tarafga qo’shing.

$$y^{2}-yc=-x^{2}+xa$$

Ikkala tarafdan y^{2} ni ayirish.

$$-yc=-x^{2}+xa-y^{2}$$

Tenglama standart shaklda.

$$\left(-y\right)c=ax-y^{2}-x^{2}$$

Ikki tarafini -y ga bo‘ling.

$$\frac{\left(-y\right)c}{-y}=\frac{ax-y^{2}-x^{2}}{-y}$$

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

$$c=\frac{ax-y^{2}-x^{2}}{-y}$$

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

$$c=\frac{x^{2}-ax}{y}+y$$