rozwiąż równania 5.158 równania wielomianowe 2x^2-13x^2+6+0 x^6-26x^3-27=0 x^4-x^2-12=0

1) [latex]2x^2-13x^2+6=0[/latex] [latex]Delta=(-13)^2-4cdot2cdot6=121 \ sqrt{Delta} =11 \ x_{1}= frac{13+11}{4} = frac{24}{4} =6 \ x_{2}= frac{13-11}{4} = frac{2}{4} = frac{1}{2} [/latex] 2) [latex]x^6-26x^3-27=0[/latex] [latex]t=x^3 \ t^2-26t-27=0 \ Delta=(-26)^2-4cdot1cdot(-27)=784 \ sqrt{Delta} =28 \ t_{1}= frac{26+28}{2} =27 \ t_{2}= frac{26-28}{2} =-1 \ x^3=27 \ oxed{x=3} \ x^3=-1 \ oxed{x=-1}[/latex] 3) [latex]x^4-x^2-12=0[/latex] [latex]t=x^2,~~ t geq 0 \ t^2-t-12=0 \ Delta=(-1)^2-4cdot1cdot(-12)=49 \ sqrt{Delta} =7\ t_{1}= frac{1+7}{2} =4 \ t_{2}= frac{1-7}{2} =-3~~ sprz. \ x^2=4 \ oxed{x=2~~ vee~~x=-2}[/latex]