ex^2=-x-3by eching

$$e x ^ { 2 } = - x - 3 b y$$

b uchun yechish (complex solution)

$$\left\{\begin{matrix}b=-\frac{x\left(ex+1\right)}{3y}\text{, }&y\neq 0\\b\in \mathrm{C}\text{, }&\left(x=0\text{ or }x=-\frac{1}{e}\right)\text{ and }y=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-x-3by=ex^{2}$$

x ni ikki tarafga qo’shing.

$$-3by=ex^{2}+x$$

Tenglama standart shaklda.

$$\left(-3y\right)b=ex^{2}+x$$

Ikki tarafini -3y ga bo‘ling.

$$\frac{\left(-3y\right)b}{-3y}=\frac{x\left(ex+1\right)}{-3y}$$

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

$$b=\frac{x\left(ex+1\right)}{-3y}$$

x\left(ex+1\right) ni -3y ga bo'lish.

$$b=-\frac{x\left(ex+1\right)}{3y}$$

b uchun yechish

$$\left\{\begin{matrix}b=-\frac{x\left(ex+1\right)}{3y}\text{, }&y\neq 0\\b\in \mathrm{R}\text{, }&\left(x=0\text{ or }x=-\frac{1}{e}\right)\text{ and }y=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$-x-3by=ex^{2}$$

x ni ikki tarafga qo’shing.

$$-3by=ex^{2}+x$$

Tenglama standart shaklda.

$$\left(-3y\right)b=ex^{2}+x$$

Ikki tarafini -3y ga bo‘ling.

$$\frac{\left(-3y\right)b}{-3y}=\frac{x\left(ex+1\right)}{-3y}$$

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

$$b=\frac{x\left(ex+1\right)}{-3y}$$

x\left(ex+1\right) ni -3y ga bo'lish.

$$b=-\frac{x\left(ex+1\right)}{3y}$$

x uchun yechish (complex solution)

$$x=\frac{\sqrt{1-12eby}-1}{2e}$$

$$x=-\frac{\sqrt{1-12eby}+1}{2e}$$

x uchun yechish

$$x=\frac{\sqrt{1-12eby}-1}{2e}$$

$$x=-\frac{\sqrt{1-12eby}+1}{2e}\text{, }\left(y\geq 0\text{ or }b\geq \frac{1}{12ey}\right)\text{ and }\left(y\leq 0\text{ or }b\leq \frac{1}{12ey}\right)$$