Solve {l}{bc=a}{d=b+c}{e=2a}{text{Solvefor}f,gtext{where}}{f=d}{g=e}

$$\left. \begin{array} { l } { b c = a }\\ { d = b + c }\\ { e = 2 a }\\ { \text{Solve for } f,g \text{ where} } \\ { f = d }\\ { g = e } \end{array} \right.$$

Solve for b, c, a, d, f, g (complex solution)

$$b=\frac{\sqrt{f^{2}-2e}+f}{2}\text{, }c=\frac{-\sqrt{f^{2}-2e}+f}{2}\text{, }a=\frac{e}{2}\approx 1.359140914\text{, }d=f\text{, }f\in \mathrm{C}\text{, }g=e\approx 2.718281828$$

$$b=\frac{-\sqrt{f^{2}-2e}+f}{2}\text{, }c=\frac{\sqrt{f^{2}-2e}+f}{2}\text{, }a=\frac{e}{2}\approx 1.359140914\text{, }d=f\text{, }f\in \mathrm{C}\text{, }g=e\approx 2.718281828$$

Solve for b, c, a, d, f, g

$$b=\frac{\sqrt{f^{2}-2e}+f}{2}\text{, }c=\frac{-\sqrt{f^{2}-2e}+f}{2}\text{, }a=\frac{e}{2}\approx 1.359140914\text{, }d=f\text{, }f\in (-\infty,-\sqrt{2e}]\cup [\sqrt{2e},\infty)\text{, }g=e\approx 2.718281828\text{; }b=\frac{-\sqrt{f^{2}-2e}+f}{2}\text{, }c=\frac{\sqrt{f^{2}-2e}+f}{2}\text{, }a=\frac{e}{2}\approx 1.359140914\text{, }d=f\text{, }f\in (-\infty,-\sqrt{2e}]\cup [\sqrt{2e},\infty)\text{, }g=e\approx 2.718281828$$