Question

Quadratic Equations: Solve using formula x= -b²+ √b²-4ac/2a
a(x² + 1)= (a²+1)x , a≠0

Answer 1

$$\begin{gathered} \mathrm{a}\left({\mathrm{x}}^2+1\right)=\left({\mathrm{a}}^2+1\right)\mathrm{x} \\ {\mathrm{ax}}^2-\left({\mathrm{a}}^2+1\right)\mathrm{x}+\mathrm{a}=0 \\ \mathrm{x}=\frac{\left({\mathrm{a}}^2+1\right)\pm \sqrt{{\left({\mathrm{a}}^2+1\right)}^2-4{\mathrm{a}}^2}}{2\mathrm{a}} \\ =\frac{\left({\mathrm{a}}^2+1\right)\pm \sqrt{{\mathrm{a}}^4+1+2{\mathrm{a}}^2-4{\mathrm{a}}^2}}{2\mathrm{a}}=\frac{\left({\mathrm{a}}^2+1\right)\pm \sqrt{{\mathrm{a}}^4+1-2{\mathrm{a}}^2}}{2\mathrm{a}} \\ =\frac{\left({\mathrm{a}}^2+1\right)\pm \sqrt{{\left({\mathrm{a}}^2-1\right)}^2}}{2\mathrm{a}}=\frac{\left({\mathrm{a}}^2+1\right)\pm \left({\mathrm{a}}^2-1\right)}{2\mathrm{a}} \\ =\mathrm{a},\frac{1}{\mathrm{a}} \end{gathered}$$