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

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

A uchun yechish (complex solution)

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

Kvadrat ildizini topish bo'yicha qadamlar

\left(AB\right)^{2} ni kengaytirish.

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

Ikkala tarafdan A^{2}CD^{3} ni ayirish.

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

Shartlarni qayta saralash.

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

A'ga ega bo'lgan barcha shartlarni birlashtirish.

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

B^{2}-CD^{3} ga bo'lish B^{2}-CD^{3} ga ko'paytirishni bekor qiladi.

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

0 ni B^{2}-CD^{3} ga bo'lish.

$$A^{2}=0$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$A=0 A=0$$

Tenglama yechildi. Yechimlar bir xil.

$$A=0$$

Kvadrat tenglamalaridan foydalanish qoidalari

\left(AB\right)^{2} ni kengaytirish.

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

Ikkala tarafdan A^{2}CD^{3} ni ayirish.

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

Shartlarni qayta saralash.

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

A'ga ega bo'lgan barcha shartlarni birlashtirish.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} B^{2}-CD^{3} ni a, 0 ni b va 0 ni c bilan almashtiring.

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

0^{2} ning kvadrat ildizini chiqarish.

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

2 ni B^{2}-CD^{3} marotabaga ko'paytirish.

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

0 ni 2B^{2}-2D^{3}C ga bo'lish.

$$A=0$$

B uchun yechish (complex solution)

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

A uchun yechish

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

B uchun yechish

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