Whakaoti i te 212x+3y/2^2+y^2=9

$$\frac { 212 x + 3 y } { 2 ^ { 2 } + y ^ { 2 } } = 9$$

Whakaoti mō x (complex solution)

$$x=\frac{9y^{2}}{212}-\frac{3y}{212}+\frac{9}{53}$$

$$y\neq -2i\text{ and }y\neq 2i$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te \left(y-2i\right)\left(y+2i\right).

$$212x+3y=9\left(y-2i\right)\left(y+2i\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 9 ki te y-2i.

$$212x+3y=\left(9y-18i\right)\left(y+2i\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 9y-18i ki te y+2i ka whakakotahi i ngā kupu rite.

$$212x+3y=9y^{2}+36$$

Tangohia te 3y mai i ngā taha e rua.

$$212x=9y^{2}+36-3y$$

He hanga arowhānui tō te whārite.

$$212x=9y^{2}-3y+36$$

Whakawehea ngā taha e rua ki te 212.

$$\frac{212x}{212}=\frac{9y^{2}-3y+36}{212}$$

Mā te whakawehe ki te 212 ka wetekia te whakareanga ki te 212.

$$x=\frac{9y^{2}-3y+36}{212}$$

Whakawehe 9y^{2}+36-3y ki te 212.

$$x=\frac{9y^{2}}{212}-\frac{3y}{212}+\frac{9}{53}$$

Whakaoti mō x

$$x=\frac{9y^{2}}{212}-\frac{3y}{212}+\frac{9}{53}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te y^{2}+4.

$$212x+3y=9\left(y^{2}+4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 9 ki te y^{2}+4.

$$212x+3y=9y^{2}+36$$

Tangohia te 3y mai i ngā taha e rua.

$$212x=9y^{2}+36-3y$$

He hanga arowhānui tō te whārite.

$$212x=9y^{2}-3y+36$$

Whakawehea ngā taha e rua ki te 212.

$$\frac{212x}{212}=\frac{9y^{2}-3y+36}{212}$$

Mā te whakawehe ki te 212 ka wetekia te whakareanga ki te 212.

$$x=\frac{9y^{2}-3y+36}{212}$$

Whakawehe 9y^{2}+36-3y ki te 212.

$$x=\frac{9y^{2}}{212}-\frac{3y}{212}+\frac{9}{53}$$

Whakaoti mō y (complex solution)

$$\left\{\begin{matrix}\\y=\frac{\sqrt{848x-143}+1}{6}\text{, }&\text{unconditionally}\\y=\frac{-\sqrt{848x-143}+1}{6}\text{, }&x\neq \frac{3}{106}i\text{ and }x\neq -\frac{3}{106}i\end{matrix}\right.$$

Whakaoti mō y

$$y=\frac{-\sqrt{848x-143}+1}{6}$$

$$y=\frac{\sqrt{848x-143}+1}{6}\text{, }x\geq \frac{143}{848}$$