حل left(y*xright)^2=sqrt{left|x!yright|}

$${ \left(y \times x \right) }^{ 2 } = \sqrt{ \left| x ! y \right| }$$

برای y حل کنید

$$\left\{\begin{matrix}y=0\text{, }&-x!\geq 0\text{ or }x!\geq 0\\y=-\frac{\sqrt[3]{x!}}{x^{\frac{4}{3}}}\text{; }y=\frac{\sqrt[3]{x!}}{x^{\frac{4}{3}}}\text{, }&\left(\frac{\sqrt[3]{x!}}{x^{\frac{4}{3}}}\geq 0\text{ and }x\neq 0\text{ and }x!\geq 0\right)\text{ or }\left(-x!\geq 0\text{ and }\frac{\sqrt[3]{x!}}{x^{\frac{4}{3}}}\leq 0\text{ and }x!\leq 0\right)\end{matrix}\right.$$