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

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

Resolver A (complex solution)

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

Pasos para obter a raíz cadrada

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

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

Resta A^{2}CD^{3} en ambos lados.

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

Reordena os termos.

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

Combina todos os termos que conteñan A.

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

A división entre B^{2}-CD^{3} desfai a multiplicación por B^{2}-CD^{3}.

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

Divide 0 entre B^{2}-CD^{3}.

$$A^{2}=0$$

Obtén a raíz cadrada de ambos lados da ecuación.

$$A=0 A=0$$

A ecuación está resolta. As solucións son iguais.

$$A=0$$

Pasos que usan a fórmula cadrática

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

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

Resta A^{2}CD^{3} en ambos lados.

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

Reordena os termos.

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

Combina todos os termos que conteñan A.

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

Esta ecuación ten unha forma estándar: ax^{2}+bx+c=0. Substitúe a por B^{2}-CD^{3}, b por 0 e c por 0 na fórmula cadrática, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Obtén a raíz cadrada de 0^{2}.

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

Multiplica 2 por B^{2}-CD^{3}.

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

Divide 0 entre 2B^{2}-2D^{3}C.

$$A=0$$

Resolver B (complex solution)

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

Resolver A

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

Resolver B

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