[tex]\left \{ {{x+y-3=0} \atop {y=x^2-5x+4}} \right. \\\left \{ {{y=-x+3} \atop {-x+3=x^2-5x+4}} \right. \\\left \{ {{y=-x+3} \atop {x^2-4x+1=0}} \right. \\\Delta=(-4)^2-4*1*1=16-4=12\\\sqrt\Delta=\sqrt{12}=\sqrt{4*3}=2\sqrt3\\x_1=\frac{4-2\sqrt3}{2}=2-\sqrt3\\x_2=\frac{4+2\sqrt3}{2}=2+\sqrt3\\\left \{ {{x=2-\sqrt3} \atop {y=-2+\sqrt3+3}} \right. \vee \left \{ {{x=2+\sqrt3} \atop {y=-2-\sqrt3+3}} \right. \\[/tex]
[tex]\left \{ {{x=2-\sqrt3} \atop {y=1+\sqrt3}} \right. \vee \left \{ {{x=2+\sqrt3} \atop {y=1-\sqrt3}} \right.[/tex]
