Zadanie 1.
[tex]\left \{ {{y=x+2} \atop {y=x^2}} \right. \\\left \{ {{x^2=x+2} \atop {y=x^2}} \right. \\\left \{ {{x^2-x-2=0} \atop {y=x^2}} \right.\\\Delta=(-1)^2-4*1*(-2)=1+8=9\\\sqrt\Delta=3\\\left \{ {{x=\frac{1-3}{2}} \atop {y=x^2}} \right. \vee \left \{ {{x=\frac{1+3}{2}} \atop {y=x^2}} \right. \\\left \{ {{x=-1} \atop {y=1}} \right. \vee \left \{ {{x=2} \atop {y=4}} \right.[/tex]
Pierwsze równanie przedstawia prostą, a drugie równanie przedstawia parabolę. Rozwiązaniem układu równań są 2 punkty (-1,1) i (2,4).
Zadanie 2.
[tex]\left \{ {{y=-\frac{1}{4}x^2+4} \atop {y=\frac{1}{4}x^2+x}} \right. \\\left \{ {{\frac{1}{4}x^2+x=-\frac{1}{4}x^2+4} \atop {y=\frac{1}{4}x^2+x}} \right. \\\left \{ {{\frac{1}{2}x^2+x-4=0\ |*2} \atop {y=\frac{1}{4}x^2+x}} \right. \\\left \{ {{x^2+2x-8=0} \atop {y=\frac{1}{4}x^2+x}} \right. \\\Delta=2^2-4*1*(-8)=4+32=36\\\sqrt\Delta=6[/tex]
[tex]\left \{ {{x=\frac{-2-6}{2}} \atop {y=\frac{1}{4}x^2+x}} \right. \vee \left \{ {{x=\frac{-2+6}{2}} \atop {y=\frac{1}{4}x^2+x}} \right. \\\left \{ {{x=-4} \atop {y=\frac{1}{4}*(-4)^2-4}} \right. \vee \left \{ {{x=2} \atop {y=\frac{1}{4}*2^2+2}} \right. \\\left \{ {{x=-4} \atop {y=0}} \right. \vee \left \{ {{x=2} \atop {y=3}} \right.[/tex]
