c^2-3xy+2y^2=0 eching

$$c ^ { 2 } - 3 x y + 2 y ^ { 2 } = 0$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=\frac{c^{2}}{3y}+\frac{2y}{3}\text{, }&y\neq 0\\x\in \mathrm{C}\text{, }&c=0\text{ and }y=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$-3xy+2y^{2}=-c^{2}$$

Ikkala tarafdan 2y^{2} ni ayirish.

$$-3xy=-c^{2}-2y^{2}$$

Tenglama standart shaklda.

$$\left(-3y\right)x=-2y^{2}-c^{2}$$

Ikki tarafini -3y ga bo‘ling.

$$\frac{\left(-3y\right)x}{-3y}=\frac{-2y^{2}-c^{2}}{-3y}$$

-3y ga bo'lish -3y ga ko'paytirishni bekor qiladi.

$$x=\frac{-2y^{2}-c^{2}}{-3y}$$

-c^{2}-2y^{2} ni -3y ga bo'lish.

$$x=\frac{c^{2}}{3y}+\frac{2y}{3}$$

x uchun yechish

$$\left\{\begin{matrix}x=\frac{c^{2}}{3y}+\frac{2y}{3}\text{, }&y\neq 0\\x\in \mathrm{R}\text{, }&c=0\text{ and }y=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

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

$$-3xy+2y^{2}=-c^{2}$$

Ikkala tarafdan 2y^{2} ni ayirish.

$$-3xy=-c^{2}-2y^{2}$$

Tenglama standart shaklda.

$$\left(-3y\right)x=-2y^{2}-c^{2}$$

Ikki tarafini -3y ga bo‘ling.

$$\frac{\left(-3y\right)x}{-3y}=\frac{-2y^{2}-c^{2}}{-3y}$$

-3y ga bo'lish -3y ga ko'paytirishni bekor qiladi.

$$x=\frac{-2y^{2}-c^{2}}{-3y}$$

-c^{2}-2y^{2} ni -3y ga bo'lish.

$$x=\frac{c^{2}}{3y}+\frac{2y}{3}$$

c uchun yechish (complex solution)

$$c=-i\sqrt{y}\sqrt{2y-3x}$$

$$c=i\sqrt{y}\sqrt{2y-3x}$$

c uchun yechish

$$c=\sqrt{y\left(3x-2y\right)}$$

$$c=-\sqrt{y\left(3x-2y\right)}\text{, }\left(y\leq 0\text{ or }x\geq \frac{2y}{3}\right)\text{ and }\left(y\geq 0\text{ or }x\leq \frac{2y}{3}\right)$$