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

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

a uchun yechish (complex solution)

$$\left\{\begin{matrix}a=-1+\frac{1}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&x=1\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan 2x ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

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

1 ni ikki tarafga qo’shing.

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

x^{2} ni ikki tarafga qo’shing.

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

a'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Tenglama standart shaklda.

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

Ikki tarafini -x^{2}+x ga bo‘ling.

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

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

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

\left(x-1\right)^{2} ni -x^{2}+x ga bo'lish.

$$a=-1+\frac{1}{x}$$

a uchun yechish

$$\left\{\begin{matrix}a=-1+\frac{1}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=1\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan 2x ni ayirish. Har qanday sonni noldan ayirsangiz, o‘zining manfiyi chiqadi.

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

1 ni ikki tarafga qo’shing.

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

x^{2} ni ikki tarafga qo’shing.

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

a'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Tenglama standart shaklda.

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

Ikki tarafini -x^{2}+x ga bo‘ling.

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

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

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

\left(x-1\right)^{2} ni -x^{2}+x ga bo'lish.

$$a=-1+\frac{1}{x}$$

x uchun yechish

$$\left\{\begin{matrix}\\x=1\text{, }&\text{unconditionally}\\x=\frac{1}{a+1}\text{, }&a\neq -1\end{matrix}\right,$$