(x+b)(2x-1)=2x^2+ax-2 eching

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

a uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x+b ga 2x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}-x+2bx-b=2x^{2}+ax-2$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$2x^{2}+ax-2=2x^{2}-x+2bx-b$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$ax-2=2x^{2}-x+2bx-b-2x^{2}$$

0 ni olish uchun 2x^{2} va -2x^{2} ni birlashtirish.

$$ax-2=-x+2bx-b$$

2 ni ikki tarafga qo’shing.

$$ax=-x+2bx-b+2$$

Tenglama standart shaklda.

$$xa=2bx-x-b+2$$

Ikki tarafini x ga bo‘ling.

$$\frac{xa}{x}=\frac{2bx-x-b+2}{x}$$

x ga bo'lish x ga ko'paytirishni bekor qiladi.

$$a=\frac{2bx-x-b+2}{x}$$

b uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x+b ga 2x-1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$2x^{2}-x+2bx-b=2x^{2}+ax-2$$

Ikkala tarafdan 2x^{2} ni ayirish.

$$-x+2bx-b=2x^{2}+ax-2-2x^{2}$$

0 ni olish uchun 2x^{2} va -2x^{2} ni birlashtirish.

$$-x+2bx-b=ax-2$$

x ni ikki tarafga qo’shing.

$$2bx-b=ax-2+x$$

b'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(2x-1\right)b=ax-2+x$$

Tenglama standart shaklda.

$$\left(2x-1\right)b=ax+x-2$$

Ikki tarafini 2x-1 ga bo‘ling.

$$\frac{\left(2x-1\right)b}{2x-1}=\frac{ax+x-2}{2x-1}$$

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

$$b=\frac{ax+x-2}{2x-1}$$