Ratkaise {x}^frac{3{2}}+{y}^frac{2{3}}=1

$${ x }^{ \frac{ 3 }{ 2 } } + { y }^{ \frac{ 2 }{ 3 } } =1$$

Ratkaise muuttujan x suhteen (complex solution)

$$x=\left(1-y^{\frac{2}{3}}\right)^{2}$$

$$y=1\text{ or }arg(1-y^{\frac{2}{3}})<\pi$$

Ratkaise muuttujan y suhteen (complex solution)

$$\left\{\begin{matrix}y=\left(1-x^{\frac{3}{2}}\right)^{3}\text{, }&arg(1-x^{\frac{3}{2}})<\frac{2\pi }{3}\\y=0\text{, }&x=1\text{ or }x=\frac{-\sqrt{3}i-1}{2}\end{matrix}\right,$$

Ratkaise muuttujan x suhteen

$$x=\left(1-y^{\frac{2}{3}}\right)^{\frac{2}{3}}$$

$$1-y^{\frac{2}{3}}\geq 0$$

Ratkaise muuttujan y suhteen

$$y=\left(1-x^{\frac{3}{2}}\right)^{\frac{3}{2}}$$

$$y=-\left(1-x^{\frac{3}{2}}\right)^{\frac{3}{2}}\text{, }x\geq 0\text{ and }x\leq 1$$