Whakaoti i te u=2x-x^3+3xyA

$$u = 2 x - x ^ { 3 } + 3 x y A$$

Whakaoti mō A (complex solution)

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

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$2x-x^{3}+3xyA=u$$

Tangohia te 2x mai i ngā taha e rua.

$$-x^{3}+3xyA=u-2x$$

Me tāpiri te x^{3} ki ngā taha e rua.

$$3xyA=u-2x+x^{3}$$

He hanga arowhānui tō te whārite.

$$3xyA=x^{3}-2x+u$$

Whakawehea ngā taha e rua ki te 3xy.

$$\frac{3xyA}{3xy}=\frac{x^{3}-2x+u}{3xy}$$

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

$$A=\frac{x^{3}-2x+u}{3xy}$$

Whakaoti mō A

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

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$2x-x^{3}+3xyA=u$$

Tangohia te 2x mai i ngā taha e rua.

$$-x^{3}+3xyA=u-2x$$

Me tāpiri te x^{3} ki ngā taha e rua.

$$3xyA=u-2x+x^{3}$$

He hanga arowhānui tō te whārite.

$$3xyA=x^{3}-2x+u$$

Whakawehea ngā taha e rua ki te 3xy.

$$\frac{3xyA}{3xy}=\frac{x^{3}-2x+u}{3xy}$$

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

$$A=\frac{x^{3}-2x+u}{3xy}$$

Whakaoti mō u

$$u=-x\left(x^{2}-3Ay-2\right)$$