Question

Помогите решить уравнение.

Answer 1

$x^{2}-x+\sqrt{x^{2}-x+4 }=2\\\\x^{2}-x-2+\sqrt{x^{2}-x+4 }=0\\\\\sqrt{x^{2}-x+4} =m,m\geq0\Rightarrow x^{2}-x+4=m^{2} \Rightarrow\\\\x^{2}-x-2 =m^{2} -6\\\\m^{2}-6+m=0\\\\m^{2}+m-6=0\\\\m_{1}=2-teorema.Vieta\\\\m_{2}=-3<0-neyd\\\\(\sqrt{x^{2}-x+4 })^{2} =2^{2}\\\\x^{2}-x+4=4\\\\x^{2}-x=0\\\\x(x-1)=0\\\\x_{1}=0\\\\x-1=0\\\\x_{2}=1\\\\Otvet:\boxed{0;1}$