Lahenda f(x)=x^2-3xyg(x)=-x^2+5x

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

Lahendage ja leidke g

$$\left\{\begin{matrix}g=\frac{2x-5}{3xy}\text{, }&y\neq 0\text{ and }x\neq 0\\g\in \mathrm{R}\text{, }&x=0\text{ or }\left(x=\frac{5}{2}\text{ and }y=0\right)\end{matrix}\right,$$

Juhised lineaarvõrrandi lahendamiseks

Korrutage x ja x, et leida x^{2}.

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

Lahutage mõlemast poolest x^{2}.

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

Kombineerige -x^{2} ja -x^{2}, et leida -2x^{2}.

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

Võrrand on standardkujul.

$$\left(-3yx^{2}\right)g=5x-2x^{2}$$

Jagage mõlemad pooled -3x^{2}y-ga.

$$\frac{\left(-3yx^{2}\right)g}{-3yx^{2}}=\frac{x\left(5-2x\right)}{-3yx^{2}}$$

-3x^{2}y-ga jagamine võtab -3x^{2}y-ga korrutamise tagasi.

$$g=\frac{x\left(5-2x\right)}{-3yx^{2}}$$

Jagage x\left(5-2x\right) väärtusega -3x^{2}y.

$$g=-\frac{5-2x}{3xy}$$

Lahendage ja leidke x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\frac{5}{2-3gy}\text{, }&g=0\text{ or }y\neq \frac{2}{3g}\end{matrix}\right,$$