f(x)=3x^2-5x-2quadyquadg(x)=2x-3 eching

$$f ( x ) = 3 x ^ { 2 } - 5 x - 2 \quad y \quad g ( x ) = 2 x - 3$$

g uchun yechish (complex solution)

$$\left\{\begin{matrix}g=\frac{3x^{2}-7x+3}{2xy}\text{, }&x\neq 0\text{ and }y\neq 0\\g\in \mathrm{C}\text{, }&\left(x=\frac{7-\sqrt{13}}{6}\text{ or }x=\frac{\sqrt{13}+7}{6}\right)\text{ and }y=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan 3x^{2} ni ayirish.

$$-5x-2ygx=2x-3-3x^{2}$$

5x ni ikki tarafga qo’shing.

$$-2ygx=2x-3-3x^{2}+5x$$

7x ni olish uchun 2x va 5x ni birlashtirish.

$$-2ygx=7x-3-3x^{2}$$

Tenglama standart shaklda.

$$\left(-2xy\right)g=-3x^{2}+7x-3$$

Ikki tarafini -2yx ga bo‘ling.

$$\frac{\left(-2xy\right)g}{-2xy}=\frac{-3x^{2}+7x-3}{-2xy}$$

-2yx ga bo'lish -2yx ga ko'paytirishni bekor qiladi.

$$g=\frac{-3x^{2}+7x-3}{-2xy}$$

-3x^{2}+7x-3 ni -2yx ga bo'lish.

$$g=-\frac{-3x^{2}+7x-3}{2xy}$$

g uchun yechish

$$\left\{\begin{matrix}g=\frac{3x^{2}-7x+3}{2xy}\text{, }&x\neq 0\text{ and }y\neq 0\\g\in \mathrm{R}\text{, }&\left(x=\frac{7-\sqrt{13}}{6}\text{ or }x=\frac{\sqrt{13}+7}{6}\right)\text{ and }y=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Ikkala tarafdan 3x^{2} ni ayirish.

$$-5x-2ygx=2x-3-3x^{2}$$

5x ni ikki tarafga qo’shing.

$$-2ygx=2x-3-3x^{2}+5x$$

7x ni olish uchun 2x va 5x ni birlashtirish.

$$-2ygx=7x-3-3x^{2}$$

Tenglama standart shaklda.

$$\left(-2xy\right)g=-3x^{2}+7x-3$$

Ikki tarafini -2yx ga bo‘ling.

$$\frac{\left(-2xy\right)g}{-2xy}=\frac{-3x^{2}+7x-3}{-2xy}$$

-2yx ga bo'lish -2yx ga ko'paytirishni bekor qiladi.

$$g=\frac{-3x^{2}+7x-3}{-2xy}$$

7x-3-3x^{2} ni -2yx ga bo'lish.

$$g=-\frac{-3x^{2}+7x-3}{2xy}$$

x uchun yechish (complex solution)

$$x=\frac{\sqrt{28gy+4\left(gy\right)^{2}+13}}{6}+\frac{gy}{3}+\frac{7}{6}$$

$$x=-\frac{\sqrt{28gy+4\left(gy\right)^{2}+13}}{6}+\frac{gy}{3}+\frac{7}{6}$$

x uchun yechish

$$x=\frac{\sqrt{28gy+4\left(gy\right)^{2}+13}}{6}+\frac{gy}{3}+\frac{7}{6}$$

$$x=-\frac{\sqrt{28gy+4\left(gy\right)^{2}+13}}{6}+\frac{gy}{3}+\frac{7}{6}\text{, }g=0\text{ or }y\geq \frac{3|g|}{g^{2}}-\frac{7}{2g}\text{ or }y\leq -\frac{3|g|}{g^{2}}-\frac{7}{2g}$$