y=ax^2-(2a-3)x+(a-1) eching

$$y = a x ^ { 2 } - ( 2 a - 3 ) x + ( a - 1 )$$

a uchun yechish (complex solution)

$$\left\{\begin{matrix}a=-\frac{3x-y-1}{\left(x-1\right)^{2}}\text{, }&x\neq 1\\a\in \mathrm{C}\text{, }&y=2\text{ and }x=1\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

2a-3 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$y=ax^{2}-\left(2ax-3x\right)+a-1$$

2ax-3x teskarisini topish uchun har birining teskarisini toping.

$$y=ax^{2}-2ax+3x+a-1$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$ax^{2}-2ax+3x+a-1=y$$

Ikkala tarafdan 3x ni ayirish.

$$ax^{2}-2ax+a-1=y-3x$$

1 ni ikki tarafga qo’shing.

$$ax^{2}-2ax+a=y-3x+1$$

a'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{2}-2x+1\right)a=y-3x+1$$

Tenglama standart shaklda.

$$\left(x^{2}-2x+1\right)a=1+y-3x$$

Ikki tarafini x^{2}-2x+1 ga bo‘ling.

$$\frac{\left(x^{2}-2x+1\right)a}{x^{2}-2x+1}=\frac{1+y-3x}{x^{2}-2x+1}$$

x^{2}-2x+1 ga bo'lish x^{2}-2x+1 ga ko'paytirishni bekor qiladi.

$$a=\frac{1+y-3x}{x^{2}-2x+1}$$

y-3x+1 ni x^{2}-2x+1 ga bo'lish.

$$a=\frac{1+y-3x}{\left(x-1\right)^{2}}$$

a uchun yechish

$$\left\{\begin{matrix}a=-\frac{3x-y-1}{\left(x-1\right)^{2}}\text{, }&x\neq 1\\a\in \mathrm{R}\text{, }&y=2\text{ and }x=1\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

2a-3 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$y=ax^{2}-\left(2ax-3x\right)+a-1$$

2ax-3x teskarisini topish uchun har birining teskarisini toping.

$$y=ax^{2}-2ax+3x+a-1$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$ax^{2}-2ax+3x+a-1=y$$

Ikkala tarafdan 3x ni ayirish.

$$ax^{2}-2ax+a-1=y-3x$$

1 ni ikki tarafga qo’shing.

$$ax^{2}-2ax+a=y-3x+1$$

a'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(x^{2}-2x+1\right)a=y-3x+1$$

Tenglama standart shaklda.

$$\left(x^{2}-2x+1\right)a=1+y-3x$$

Ikki tarafini x^{2}-2x+1 ga bo‘ling.

$$\frac{\left(x^{2}-2x+1\right)a}{x^{2}-2x+1}=\frac{1+y-3x}{x^{2}-2x+1}$$

x^{2}-2x+1 ga bo'lish x^{2}-2x+1 ga ko'paytirishni bekor qiladi.

$$a=\frac{1+y-3x}{x^{2}-2x+1}$$

y-3x+1 ni x^{2}-2x+1 ga bo'lish.

$$a=\frac{1+y-3x}{\left(x-1\right)^{2}}$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{4ay-8a+9}+2a-3}{2a}\text{; }x=\frac{-\sqrt{4ay-8a+9}+2a-3}{2a}\text{, }&a\neq 0\\x=\frac{y+1}{3}\text{, }&a=0\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}x=\frac{\sqrt{4ay-8a+9}+2a-3}{2a}\text{; }x=\frac{-\sqrt{4ay-8a+9}+2a-3}{2a}\text{, }&\left(a>0\text{ or }y\leq 2-\frac{9}{4a}\right)\text{ and }\left(y\leq \text{Indeterminate}\text{ or }a\neq 0\right)\text{ and }\left(a<0\text{ or }\left(a\neq 0\text{ and }y\geq 2-\frac{9}{4a}\right)\right)\\x=\frac{y+1}{3}\text{, }&a=0\end{matrix}\right,$$