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

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

Réitigh do g. (complex solution)

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

Céimeanna chun Cothromóidí Líneacha a Réiteach

Bain 3x^{2} ón dá thaobh.

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

Cuir 5x leis an dá thaobh.

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

Comhcheangail 2x agus 5x chun 7x a fháil.

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

Tá an chothromóid i bhfoirm chaighdeánach.

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

Roinn an dá thaobh faoi -2yx.

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

Má roinntear é faoi -2yx cuirtear an iolrúchán faoi -2yx ar ceal.

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

Roinn -3x^{2}+7x-3 faoi -2yx.

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

Réitigh do g.

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

Céimeanna chun Cothromóidí Líneacha a Réiteach

Bain 3x^{2} ón dá thaobh.

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

Cuir 5x leis an dá thaobh.

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

Comhcheangail 2x agus 5x chun 7x a fháil.

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

Tá an chothromóid i bhfoirm chaighdeánach.

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

Roinn an dá thaobh faoi -2yx.

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

Má roinntear é faoi -2yx cuirtear an iolrúchán faoi -2yx ar ceal.

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

Roinn 7x-3-3x^{2} faoi -2yx.

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

Réitigh do x. (complex solution)

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

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

Réitigh do x.

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

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