Whakaoti i te 211x^2+2012xy+222yz+2013x+2023y+9933=0

$$211 x ^ { 2 } + 2012 x y + 222 y z + 2013 x + 2023 y + 9933 = 0$$

Whakaoti mō y (complex solution)

$$\left\{\begin{matrix}y=-\frac{211x^{2}+2013x+9933}{2012x+222z+2023}\text{, }&x\neq -\frac{111z}{1006}-\frac{2023}{2012}\\y\in \mathrm{C}\text{, }&\left(x=\frac{-\sqrt{4331283}i-2013}{422}\text{ and }z=\frac{503\sqrt{4331283}i}{23421}+\frac{1598225}{46842}\right)\text{ or }\left(x=\frac{-2013+\sqrt{4331283}i}{422}\text{ and }z=-\frac{503\sqrt{4331283}i}{23421}+\frac{1598225}{46842}\right)\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te 211x^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$2012xy+222yz+2013x+2023y+9933=-211x^{2}$$

Tangohia te 2013x mai i ngā taha e rua.

$$2012xy+222yz+2023y+9933=-211x^{2}-2013x$$

Tangohia te 9933 mai i ngā taha e rua.

$$2012xy+222yz+2023y=-211x^{2}-2013x-9933$$

Pahekotia ngā kīanga tau katoa e whai ana i te y.

$$\left(2012x+222z+2023\right)y=-211x^{2}-2013x-9933$$

Whakawehea ngā taha e rua ki te 2012x+222z+2023.

$$\frac{\left(2012x+222z+2023\right)y}{2012x+222z+2023}=\frac{-211x^{2}-2013x-9933}{2012x+222z+2023}$$

Mā te whakawehe ki te 2012x+222z+2023 ka wetekia te whakareanga ki te 2012x+222z+2023.

$$y=\frac{-211x^{2}-2013x-9933}{2012x+222z+2023}$$

Whakawehe -211x^{2}-2013x-9933 ki te 2012x+222z+2023.

$$y=-\frac{211x^{2}+2013x+9933}{2012x+222z+2023}$$

Whakaoti mō y

$$y=-\frac{211x^{2}+2013x+9933}{2012x+222z+2023}$$

$$x\neq -\frac{111z}{1006}-\frac{2023}{2012}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te 211x^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$2012xy+222yz+2013x+2023y+9933=-211x^{2}$$

Tangohia te 2013x mai i ngā taha e rua.

$$2012xy+222yz+2023y+9933=-211x^{2}-2013x$$

Tangohia te 9933 mai i ngā taha e rua.

$$2012xy+222yz+2023y=-211x^{2}-2013x-9933$$

Pahekotia ngā kīanga tau katoa e whai ana i te y.

$$\left(2012x+222z+2023\right)y=-211x^{2}-2013x-9933$$

Whakawehea ngā taha e rua ki te 2012x+222z+2023.

$$\frac{\left(2012x+222z+2023\right)y}{2012x+222z+2023}=\frac{-211x^{2}-2013x-9933}{2012x+222z+2023}$$

Mā te whakawehe ki te 2012x+222z+2023 ka wetekia te whakareanga ki te 2012x+222z+2023.

$$y=\frac{-211x^{2}-2013x-9933}{2012x+222z+2023}$$

Whakawehe -211x^{2}-2013x-9933 ki te 2012x+222z+2023.

$$y=-\frac{211x^{2}+2013x+9933}{2012x+222z+2023}$$

Whakaoti mō x (complex solution)

$$x=\frac{\sqrt{4048144y^{2}-187368yz+6392900y-4331283}}{422}-\frac{1006y}{211}-\frac{2013}{422}$$

$$x=-\frac{\sqrt{4048144y^{2}-187368yz+6392900y-4331283}}{422}-\frac{1006y}{211}-\frac{2013}{422}$$

Whakaoti mō x

$$x=\frac{\sqrt{4048144y^{2}-187368yz+6392900y-4331283}}{422}-\frac{1006y}{211}-\frac{2013}{422}$$

$$x=-\frac{\sqrt{4048144y^{2}-187368yz+6392900y-4331283}}{422}-\frac{1006y}{211}-\frac{2013}{422}\text{, }y\leq -\frac{\sqrt{\left(1598225-46842z\right)^{2}[phone]}}{2024072}+\frac{23421z}{1012036}-\frac{1598225}{2024072}\text{ or }y\geq \frac{\sqrt{\left(1598225-46842z\right)^{2}[phone]}}{2024072}+\frac{23421z}{1012036}-\frac{1598225}{2024072}$$