Riješi y=x^2-2x+4y=x+2k

$$y = x ^ { 2 } - 2 x + 4 y = x + 2 k$$

Procijeni (complex solution)

$$y=x^{2}-2x+4y\text{ and }x^{2}-2x+4y=x+2k$$

Riješite za x

$$\left\{\begin{matrix}x=-\frac{\sqrt{-24k-6\sqrt{1-24k}+10}}{2}+1\text{, }&y=2k+\frac{\sqrt{1-24k}}{2}-\frac{1}{2}\text{ and }k\geq -\frac{1}{3}\text{ and }k\leq \frac{1}{24}\\x=-\frac{\sqrt{-24k+6\sqrt{1-24k}+10}}{2}+1\text{, }&y=2k-\frac{\sqrt{1-24k}}{2}-\frac{1}{2}\text{ and }k\leq \frac{1}{24}\\x=\frac{\sqrt{-24k-6\sqrt{1-24k}+10}}{2}+1\text{, }&y=2k+\frac{\sqrt{1-24k}}{2}-\frac{1}{2}\text{ and }k\geq -\frac{5}{8}\text{ and }k\leq -\frac{1}{3}\\x=\sqrt{1-3y}+1\text{, }&y=2k+\frac{\sqrt{1-24k}}{2}-\frac{1}{2}\text{ and }k\leq -\frac{5}{8}\end{matrix}\right,$$

Riješite za y

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

$$k=-\frac{x\left(x+1\right)}{6}$$