y=-ab-2by+2b^2=? eching

$$y = - a b - 2 b y + 2 b ^ { 2 } = ?$$

a uchun yechish (complex solution)

$$\left\{\begin{matrix}a=2b-2y-\frac{y}{b}\text{, }&b\neq 0\\a\in \mathrm{C}\text{, }&b=0\text{ and }y=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\left(-a\right)b-2by+2b^{2}=y$$

2by ni ikki tarafga qo’shing.

$$\left(-a\right)b+2b^{2}=y+2by$$

Ikkala tarafdan 2b^{2} ni ayirish.

$$\left(-a\right)b=y+2by-2b^{2}$$

Shartlarni qayta saralash.

$$-ab=2by+y-2b^{2}$$

Tenglama standart shaklda.

$$\left(-b\right)a=2by+y-2b^{2}$$

Ikki tarafini -b ga bo‘ling.

$$\frac{\left(-b\right)a}{-b}=\frac{2by+y-2b^{2}}{-b}$$

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

$$a=\frac{2by+y-2b^{2}}{-b}$$

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

$$a=2b-2y-\frac{y}{b}$$

a uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\left(-a\right)b-2by+2b^{2}=y$$

2by ni ikki tarafga qo’shing.

$$\left(-a\right)b+2b^{2}=y+2by$$

Ikkala tarafdan 2b^{2} ni ayirish.

$$\left(-a\right)b=y+2by-2b^{2}$$

Shartlarni qayta saralash.

$$-ab=2by+y-2b^{2}$$

Tenglama standart shaklda.

$$\left(-b\right)a=2by+y-2b^{2}$$

Ikki tarafini -b ga bo‘ling.

$$\frac{\left(-b\right)a}{-b}=\frac{2by+y-2b^{2}}{-b}$$

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

$$a=\frac{2by+y-2b^{2}}{-b}$$

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

$$a=2b-2y-\frac{y}{b}$$

b uchun yechish (complex solution)

$$b=\frac{-\sqrt{4y^{2}+4ay+8y+a^{2}}+a+2y}{4}$$

$$b=\frac{\sqrt{4y^{2}+4ay+8y+a^{2}}+a+2y}{4}$$

b uchun yechish

$$b=\frac{-\sqrt{4y^{2}+4ay+8y+a^{2}}+a+2y}{4}$$

$$b=\frac{\sqrt{4y^{2}+4ay+8y+a^{2}}+a+2y}{4}\text{, }y\geq -\frac{a}{2}+\sqrt{a+1}-1\text{ or }y\leq -\frac{a}{2}-\sqrt{a+1}-1\text{ or }a\leq -1$$