Solve for x (complex solution)
\left\{\begin{matrix}x=\left(2020-y\right)^{2}+\frac{\sqrt{4y^{2}-16160y+16321601}}{2}+\frac{1}{2}\text{, }&arg(\frac{\sqrt{4y^{2}-16160y+16321601}+1}{2})\geq \pi \text{ and }arg(2020-y)\geq \pi \\x=\left(2020-y\right)^{2}-\frac{\sqrt{4y^{2}-16160y+16321601}}{2}+\frac{1}{2}\text{, }&y=2020\text{ or }\left(arg(\frac{-\sqrt{4y^{2}-16160y+16321601}+1}{2})\geq \pi \text{ and }arg(2020-y)\geq \pi \right)\end{matrix}\right.
Solve for y (complex solution)
y=\sqrt{x+\sqrt{x}}+2020
Solve for x
x=\left(2020-y\right)^{2}-\frac{\sqrt{4y^{2}-16160y+16321601}}{2}+\frac{1}{2}
y-2020\geq 0
Solve for y
y=\sqrt[4]{x}\sqrt{\sqrt{x}+1}+2020
x\geq 0
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