حل {l}{y=sqrt{x}+x^2}{z=-4x^2}{a=z}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { y = \sqrt{x} + x ^ {2} }\\ { z = -4 x ^ {2} }\\ { a = z }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

برای x،y،z حل کنید (complex solution)

$$\left\{\begin{matrix}x=\frac{i\sqrt{a}}{2}\text{, }y=-\frac{b}{4}+\left(\frac{1}{2}+\frac{1}{2}i\right)\sqrt[4]{b}\text{, }z=a\text{, }&\left(a=b\text{ and }arg(\left(\frac{1}{2}+\frac{1}{2}i\right)\sqrt[4]{b})<\pi \text{ and }b\neq 0\right)\text{ or }\left(a=0\text{ and }b=0\right)\\x=-\frac{i\sqrt{a}}{2}\text{, }y=-\frac{b}{4}+\left(-\frac{1}{2}+\frac{1}{2}i\right)\sqrt[4]{b}\text{, }z=a\text{, }&\left(a=b\text{ and }arg(\left(-\frac{1}{2}+\frac{1}{2}i\right)\sqrt[4]{b})<\pi \text{ and }b\neq 0\right)\text{ or }\left(a=0\text{ and }b=0\right)\\x=0\text{, }y=0\text{, }z=0\text{, }&a=0\text{ and }b=0\\x=-\frac{i\sqrt{a}}{2}\text{, }y=-\frac{b}{4}+\left(\frac{1}{2}-\frac{1}{2}i\right)\sqrt[4]{b}\text{, }z=a\text{, }&\left(a=b\text{ and }arg(\left(\frac{1}{2}-\frac{1}{2}i\right)\sqrt[4]{b})<\pi \text{ and }b\neq 0\right)\text{ or }\left(a=0\text{ and }b=0\right)\end{matrix}\right.$$

برای x،y،z حل کنید

$$\left\{\begin{matrix}x=0\text{, }y=0\text{, }z=0\text{, }&a=0\text{ and }b=0\\x=\frac{\sqrt{-a}}{2}\text{, }y=-\frac{a}{4}+\frac{\sqrt{2}\sqrt[4]{-a}}{2}\text{, }z=a\text{, }&b=a\text{ and }a\leq 0\end{matrix}\right.$$