Whakaoti i te 27=x(3y-x)-3

$$27 = x ( 3 y - x ) - 3$$

Whakaoti mō y

$$y=\frac{x}{3}+\frac{10}{x}$$

$$x\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 3y-x.

$$27=3xy-x^{2}-3$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$3xy-x^{2}-3=27$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$3xy-3=27+x^{2}$$

Me tāpiri te 3 ki ngā taha e rua.

$$3xy=27+x^{2}+3$$

Tāpirihia te 27 ki te 3, ka 30.

$$3xy=30+x^{2}$$

He hanga arowhānui tō te whārite.

$$3xy=x^{2}+30$$

Whakawehea ngā taha e rua ki te 3x.

$$\frac{3xy}{3x}=\frac{x^{2}+30}{3x}$$

Mā te whakawehe ki te 3x ka wetekia te whakareanga ki te 3x.

$$y=\frac{x^{2}+30}{3x}$$

Whakawehe 30+x^{2} ki te 3x.

$$y=\frac{x}{3}+\frac{10}{x}$$

Whakaoti mō x (complex solution)

$$x=\frac{-\sqrt{9y^{2}-120}+3y}{2}$$

$$x=\frac{\sqrt{9y^{2}-120}+3y}{2}$$

Whakaoti mō x

$$x=\frac{-\sqrt{9y^{2}-120}+3y}{2}$$

$$x=\frac{\sqrt{9y^{2}-120}+3y}{2}\text{, }|y|\geq \frac{2\sqrt{30}}{3}$$