Question Number 203675 by 073 last updated on 25/Jan/24
Answered by Frix last updated on 25/Jan/24
$${x}^{\mathrm{4}} −\mathrm{2}{ax}^{\mathrm{2}} −{x}+{a}^{\mathrm{2}} −{a}=\mathrm{0} \\ $$$$\left({x}^{\mathrm{2}} +{x}−{a}+\mathrm{1}\right)\left({x}^{\mathrm{2}} −{x}−{a}\right)=\mathrm{0} \\ $$$${x}=−\frac{\mathrm{1}}{\mathrm{2}}\pm\frac{\sqrt{\mathrm{4}{a}−\mathrm{3}}}{\mathrm{2}}\vee{x}=\frac{\mathrm{1}}{\mathrm{2}}\pm\frac{\sqrt{\mathrm{4}{a}+\mathrm{1}}}{\mathrm{2}} \\ $$