ax^2+3x-a+1=0 eching

$$a x ^ { 2 } + 3 x - a + 1 = 0$$

a uchun yechish (complex solution)

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

$$x\neq -1\text{ and }x\neq 1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan 3x ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

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

Ikkala tarafdan 1 ni ayirish.

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

a'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Ikki tarafini x^{2}-1 ga bo‘ling.

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

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

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

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

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

a uchun yechish

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

$$|x|\neq 1$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan 3x ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

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

Ikkala tarafdan 1 ni ayirish.

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

a'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Ikki tarafini x^{2}-1 ga bo‘ling.

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

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

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

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

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

x uchun yechish

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