[latex]1\ f(x)=2(x-2)(x-5)[/latex] [latex]2\ x^2-5x extgreater 6\ x^2-5x-6 extgreater 0\ (x+1)(x-6) extgreater \ \ x_{1}=-1\ x_{2}=6\ \ xin(-infty, -1)cup(6, +infty)[/latex] [latex]3\ (x-3)^3(x^2-25)(6x-6) =0\ (x-3)^3(x+5)(x-5)(x-1)6=0\ x-3=0 vee x+5=0 vee x-5=0 vee x-1=0\ x=3 vee x=-5 vee x=5 vee x=1[/latex]
Zad. 1 [latex]f(x)=2x^{2}-14x+20=2(x^{2}-7x+10)=2(x^{2}-2x-5x+10)= \ \ =2[x(x-2)-5(x-2)]=2(x-5)(x-2)[/latex] Zad. 2 [latex]x^{2}-5x extgreater -6 \ \ x^{2}-5x+6 extgreater 0 \ \ Delta=(-5)^{2}-4*1*6=25-24=1 \ \ sqrt{Delta}=1 \ \ x_{1}= frac{5-1}{2}=2 \ \ x_{2}= frac{5+1}{2}=3 \ \ xin (-infty,2) vee (3,infty) [/latex] Zad. 3 [latex](x-3)^{3}(x^{2}-25)(6x-6)=0 \ \ (x-3)^{3}(x-5)(x+5)6(x-1)=0 \ \ x-3=0 vee x-5=0 vee x+5=0 vee x-1=0 \ \ x=3 vee x=5 vee x=-5 vee x=1 \ \ xin lbrace -5,1,3,5 brace[/latex]
