Whakaoti i te (2x^3-4y^3)^2=dy

$$( 2 x ^ { 3 } - 4 y ^ { 3 } ) ^ { 2 } = d y$$

Whakaoti mō d (complex solution)

$$\left\{\begin{matrix}d=\frac{4\left(x^{3}-2y^{3}\right)^{2}}{y}\text{, }&y\neq 0\\d\in \mathrm{C}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(2x^{3}-4y^{3}\right)^{2}.

$$4\left(x^{3}\right)^{2}-16x^{3}y^{3}+16\left(y^{3}\right)^{2}=dy$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 3 me te 2 kia riro ai te 6.

$$4x^{6}-16x^{3}y^{3}+16\left(y^{3}\right)^{2}=dy$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 3 me te 2 kia riro ai te 6.

$$4x^{6}-16x^{3}y^{3}+16y^{6}=dy$$

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

$$dy=4x^{6}-16x^{3}y^{3}+16y^{6}$$

He hanga arowhānui tō te whārite.

$$yd=4x^{6}-16x^{3}y^{3}+16y^{6}$$

Whakawehea ngā taha e rua ki te y.

$$\frac{yd}{y}=\frac{4\left(x^{3}-2y^{3}\right)^{2}}{y}$$

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

$$d=\frac{4\left(x^{3}-2y^{3}\right)^{2}}{y}$$

Whakaoti mō d

$$\left\{\begin{matrix}d=\frac{4\left(x^{3}-2y^{3}\right)^{2}}{y}\text{, }&y\neq 0\\d\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(2x^{3}-4y^{3}\right)^{2}.

$$4\left(x^{3}\right)^{2}-16x^{3}y^{3}+16\left(y^{3}\right)^{2}=dy$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 3 me te 2 kia riro ai te 6.

$$4x^{6}-16x^{3}y^{3}+16\left(y^{3}\right)^{2}=dy$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 3 me te 2 kia riro ai te 6.

$$4x^{6}-16x^{3}y^{3}+16y^{6}=dy$$

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

$$dy=4x^{6}-16x^{3}y^{3}+16y^{6}$$

He hanga arowhānui tō te whārite.

$$yd=4x^{6}-16x^{3}y^{3}+16y^{6}$$

Whakawehea ngā taha e rua ki te y.

$$\frac{yd}{y}=\frac{4\left(x^{3}-2y^{3}\right)^{2}}{y}$$

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

$$d=\frac{4\left(x^{3}-2y^{3}\right)^{2}}{y}$$

Whakaoti mō x (complex solution)

$$x\in \frac{2^{\frac{2}{3}}\sqrt[3]{\sqrt{y}\left(4y^{\frac{5}{2}}+\sqrt{d}\right)}}{2},\frac{2^{\frac{2}{3}}e^{\frac{4\pi i}{3}}\sqrt[3]{\sqrt{y}\left(4y^{\frac{5}{2}}+\sqrt{d}\right)}}{2},\frac{2^{\frac{2}{3}}e^{\frac{2\pi i}{3}}\sqrt[3]{\sqrt{y}\left(4y^{\frac{5}{2}}+\sqrt{d}\right)}}{2},\frac{2^{\frac{2}{3}}e^{\frac{4\pi i}{3}}\sqrt[3]{\sqrt{y}\left(4y^{\frac{5}{2}}-\sqrt{d}\right)}}{2},\frac{2^{\frac{2}{3}}\sqrt[3]{\sqrt{y}\left(4y^{\frac{5}{2}}-\sqrt{d}\right)}}{2},\frac{2^{\frac{2}{3}}e^{\frac{2\pi i}{3}}\sqrt[3]{\sqrt{y}\left(4y^{\frac{5}{2}}-\sqrt{d}\right)}}{2}$$

Whakaoti mō x

$$\left\{\begin{matrix}x=\frac{2^{\frac{2}{3}}\sqrt[3]{4y^{3}-\sqrt{dy}}}{2}\text{; }x=\frac{2^{\frac{2}{3}}\sqrt[3]{4y^{3}+\sqrt{dy}}}{2}\text{, }&d\leq 0\text{ and }y\leq 0\\x=\frac{2^{\frac{2}{3}}\sqrt[6]{y}\sqrt[3]{4y^{\frac{5}{2}}-\sqrt{d}}}{2}\text{; }x=\frac{2^{\frac{2}{3}}\sqrt[6]{y}\sqrt[3]{4y^{\frac{5}{2}}+\sqrt{d}}}{2}\text{, }&y\geq 0\text{ and }d\geq 0\end{matrix}\right.$$