გადაწყვიტეთ x^frac{5{2}}+y^frac{5{2}}=1000

$$x ^ { \frac { 5 } { 2 } } + y ^ { \frac { 5 } { 2 } } = 1000$$

ამოხსნა x-ისთვის (complex solution)

$$\left\{\begin{matrix}x=\left(1000-y^{\frac{5}{2}}\right)^{2}\text{, }&arg(\left(\left(1000-y^{\frac{5}{2}}\right)^{2}\right)^{\frac{5}{2}})<\pi \text{ and }arg(1000-y^{\frac{5}{2}})<\pi \\x=0\text{, }&y=10^{\frac{6}{5}}e^{\frac{8\pi i}{5}}\text{ or }y=10^{\frac{6}{5}}e^{\frac{4\pi i}{5}}\text{ or }y=10^{\frac{6}{5}}\end{matrix}\right.$$

ამოხსნა y-ისთვის (complex solution)

$$\left\{\begin{matrix}y=\left(1000-x^{\frac{5}{2}}\right)^{2}\text{, }&arg(y^{\frac{5}{2}})<\pi \text{ and }arg(1000-x^{\frac{5}{2}})<\pi \\y=0\text{, }&x=10^{\frac{6}{5}}e^{\frac{8\pi i}{5}}\text{ or }x=10^{\frac{6}{5}}e^{\frac{4\pi i}{5}}\text{ or }x=10^{\frac{6}{5}}\end{matrix}\right.$$

ამოხსნა x-ისთვის

$$x=\left(1000-y^{\frac{5}{2}}\right)^{\frac{2}{5}}$$

$$y\geq 0\text{ and }1000-y^{\frac{5}{2}}\geq 0$$

ამოხსნა y-ისთვის

$$y=\left(1000-x^{\frac{5}{2}}\right)^{\frac{2}{5}}$$

$$x\geq 0\text{ and }1000-x^{\frac{5}{2}}\geq 0$$