Решете (a^{2}-b^2)x^2-4abx+b^2=a^2

$$( a ^ { 2 } - b ^ { 2 } ) x ^ { 2 } - 4 a b x + b ^ { 2 } = a ^ { 2 }$$

Решаване за a (complex solution)

$$\left\{\begin{matrix}a=-\frac{\sqrt{\left(b\left(x^{2}+1\right)\right)^{2}}+2bx}{1-x^{2}}\text{; }a=-\frac{-\sqrt{\left(b\left(x^{2}+1\right)\right)^{2}}+2bx}{1-x^{2}}\text{, }&x\neq 1\text{ and }x\neq -1\\a=\frac{b\left(1-x^{2}\right)}{4x}\text{, }&b\neq 0\text{ and }\left(x=1\text{ or }x=-1\right)\\a\in \mathrm{C}\text{, }&\left(x=-1\text{ or }x=1\right)\text{ and }b=0\end{matrix}\right,$$

Решаване за b (complex solution)

$$\left\{\begin{matrix}b=\frac{\sqrt{\left(a\left(x^{2}+1\right)\right)^{2}}+2ax}{1-x^{2}}\text{; }b=\frac{-\sqrt{\left(a\left(x^{2}+1\right)\right)^{2}}+2ax}{1-x^{2}}\text{, }&x\neq 1\text{ and }x\neq -1\\b=-\frac{a\left(1-x^{2}\right)}{4x}\text{, }&a\neq 0\text{ and }\left(x=1\text{ or }x=-1\right)\\b\in \mathrm{C}\text{, }&\left(x=-1\text{ or }x=1\right)\text{ and }a=0\end{matrix}\right,$$

Решаване за a

$$\left\{\begin{matrix}a=\frac{b\left(x+1\right)}{x-1}\text{; }a=\frac{b\left(1-x\right)}{x+1}\text{, }&|x|\neq 1\\a=\frac{b\left(1-x^{2}\right)}{4x}\text{, }&b\neq 0\text{ and }|x|=1\\a\in \mathrm{R}\text{, }&b=0\text{ and }|x|=1\end{matrix}\right,$$

Решаване за b

$$\left\{\begin{matrix}b=\frac{a\left(x+1\right)}{1-x}\text{; }b=-\frac{a\left(1-x\right)}{x+1}\text{, }&|x|\neq 1\\b=\frac{a\left(x^{2}-1\right)}{4x}\text{, }&a\neq 0\text{ and }|x|=1\\b\in \mathrm{R}\text{, }&a=0\text{ and }|x|=1\end{matrix}\right,$$