Решете k^2x^2+(4k^2-8)x+4k^2=0

$$k ^ { 2 } x ^ { 2 } + ( 4 k ^ { 2 } - 8 ) x + 4 k ^ { 2 } = 0$$

Решаване за k (complex solution)

$$k=-\frac{2\sqrt{2x}}{x+2}$$

$$k=\frac{2\sqrt{2x}}{x+2}\text{, }x\neq -2$$

Решаване за x (complex solution)

$$\left\{\begin{matrix}x=-2+\frac{4\sqrt{1-k^{2}}}{k^{2}}+\frac{4}{k^{2}}\text{; }x=-2-\frac{4\sqrt{1-k^{2}}}{k^{2}}+\frac{4}{k^{2}}\text{, }&k\neq 0\\x=0\text{, }&k=0\end{matrix}\right,$$

Решаване за k

$$k=\frac{2\sqrt{2x}}{x+2}$$

$$k=-\frac{2\sqrt{2x}}{x+2}\text{, }x\geq 0$$

Решаване за x

$$\left\{\begin{matrix}x=-2+\frac{4\sqrt{1-k^{2}}}{k^{2}}+\frac{4}{k^{2}}\text{; }x=-2-\frac{4\sqrt{1-k^{2}}}{k^{2}}+\frac{4}{k^{2}}\text{, }&k\neq 0\text{ and }|k|\leq 1\\x=0\text{, }&k=0\end{matrix}\right,$$