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Question-203675




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

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