Resolver (A*B)^2=A^2*CD^3

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

Ebatzi: A (complex solution)

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

Erro karratua bilatzeko urratsak

Garatu \left(AB\right)^{2}.

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

Kendu A^{2}CD^{3} bi aldeetatik.

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

Berrantolatu gaiak.

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

Konbinatu A duten gai guztiak.

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

B^{2}-CD^{3} balioarekin zatituz gero, B^{2}-CD^{3} balioarekiko biderketa desegiten da.

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

Zatitu 0 balioa B^{2}-CD^{3} balioarekin.

$$A^{2}=0$$

Atera ekuazioaren bi aldeen erro karratua.

$$A=0 A=0$$

Ebatzi da ekuazioa. Soluzioak berdinak dira.

$$A=0$$

Formula koadratikoaren bidezko ebazpidea

Garatu \left(AB\right)^{2}.

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

Kendu A^{2}CD^{3} bi aldeetatik.

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

Berrantolatu gaiak.

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

Konbinatu A duten gai guztiak.

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

Estandarra da ekuazioaren forma: ax^{2}+bx+c=0. Ordeztu B^{2}-CD^{3} balioa a balioarekin, 0 balioa b balioarekin, eta 0 balioa c balioarekin formula koadratikoan (\frac{-b±\sqrt{b^{2}-4ac}}{2a}).

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

Atera 0^{2} balioaren erro karratua.

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

Egin 2 bider B^{2}-CD^{3}.

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

Zatitu 0 balioa 2B^{2}-2D^{3}C balioarekin.

$$A=0$$

Ebatzi: B (complex solution)

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

Ebatzi: A

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

Ebatzi: B

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