Whakaoti i te (A*B)^2=A^2*CD^3

$$( A \times B ) ^ { 2 } = A ^ { 2 } \times C D ^ { 3 }$$

Whakaoti mō A (complex solution)

$$\left\{\begin{matrix}\\A=0\text{, }&\text{unconditionally}\\A\in \mathrm{C}\text{, }&B=-\sqrt{C}D^{\frac{3}{2}}\text{ or }B=\sqrt{C}D^{\frac{3}{2}}\end{matrix}\right.$$

Ngā Upane mā te Kimi Pūtakerua

Whakarohaina te \left(AB\right)^{2}.

$$A^{2}B^{2}=A^{2}CD^{3}$$

Tangohia te A^{2}CD^{3} mai i ngā taha e rua.

$$A^{2}B^{2}-A^{2}CD^{3}=0$$

Whakaraupapatia anō ngā kīanga tau.

$$A^{2}B^{2}-CA^{2}D^{3}=0$$

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

$$\left(B^{2}-CD^{3}\right)A^{2}=0$$

Mā te whakawehe ki te B^{2}-CD^{3} ka wetekia te whakareanga ki te B^{2}-CD^{3}.

$$A^{2}=\frac{0}{B^{2}-CD^{3}}$$

Whakawehe 0 ki te B^{2}-CD^{3}.

$$A^{2}=0$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$A=0 A=0$$

Kua oti te whārite te whakatau. He ōrite ngā whakatau.

$$A=0$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakarohaina te \left(AB\right)^{2}.

$$A^{2}B^{2}=A^{2}CD^{3}$$

Tangohia te A^{2}CD^{3} mai i ngā taha e rua.

$$A^{2}B^{2}-A^{2}CD^{3}=0$$

Whakaraupapatia anō ngā kīanga tau.

$$A^{2}B^{2}-CA^{2}D^{3}=0$$

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

$$\left(B^{2}-CD^{3}\right)A^{2}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi B^{2}-CD^{3} mō a, 0 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$A=\frac{0±\sqrt{0^{2}}}{2\left(B^{2}-CD^{3}\right)}$$

Tuhia te pūtakerua o te 0^{2}.

$$A=\frac{0±0}{2\left(B^{2}-CD^{3}\right)}$$

Whakareatia 2 ki te B^{2}-CD^{3}.

$$A=\frac{0}{2B^{2}-2CD^{3}}$$

Whakawehe 0 ki te 2B^{2}-2D^{3}C.

$$A=0$$

Whakaoti mō B (complex solution)

$$\left\{\begin{matrix}\\B=-\sqrt{C}D^{\frac{3}{2}}\text{; }B=\sqrt{C}D^{\frac{3}{2}}\text{, }&\text{unconditionally}\\B\in \mathrm{C}\text{, }&A=0\end{matrix}\right.$$

Whakaoti mō A

$$\left\{\begin{matrix}\\A=0\text{, }&\text{unconditionally}\\A\in \mathrm{R}\text{, }&\left(B=0\text{ and }C=0\text{ and }D=0\right)\text{ or }\left(C\geq 0\text{ and }D\geq 0\text{ and }|B|=\sqrt{CD^{3}}\right)\text{ or }\left(D\leq 0\text{ and }C\leq 0\text{ and }|B|=\sqrt{CD^{3}}\right)\end{matrix}\right.$$

Whakaoti mō B

$$\left\{\begin{matrix}B\in \mathrm{R}\text{, }&A=0\\B=-\sqrt{CD^{3}}\text{; }B=\sqrt{CD^{3}}\text{, }&A\neq 0\text{ and }D\leq 0\text{ and }C\leq 0\\B=-\sqrt{C}D^{\frac{3}{2}}\text{; }B=\sqrt{C}D^{\frac{3}{2}}\text{, }&A\neq 0\text{ and }C\geq 0\text{ and }D\geq 0\end{matrix}\right.$$