Rozwiąż równania i nierówności: 1.[latex] 25x^{4}-10x^{2}+1=0 [/latex] 2.[latex] x^{3} -6 x^{2} -2x+12=0[/latex] 3. [latex] x^{2} +x-12>0[/latex] 3.[latex]-2 x^{2} +5x-2 geq 0[/latex] 4.[latex] frac{x(x-2)}{3}+4= frac{(2x-3)(x-1)-1}{6}+2x [/latex]

[latex]1.\ 25x^4-10x^2+1=0\ (5x^2-1)^2=0\ (sqrt{5}+1)(sqrt{5}-1)=0\ sqrt{5}x+1=0 vee sqrt{5}x-1=0\ x=-frac{1}{sqrt{5}}=-frac{sqrt{5}}{5} vee x=frac{1}{sqrt{5}}=frac{sqrt{5}}{5}\ \2\ x^3-6x^2-2x+12=0\ x^2(x-6)-2(x-6)=0\ (x^2-2)(x-6)=0\ (x+sqrt{2})(x-sqrt{2})(x-6)=0\ x+sqrt{2}=0 vee x-sqrt{2}=0 vee x-6=0\ x=-sqrt{2} vee x=sqrt{2} vee x=6[/latex] [latex]3\-2x^2+5x-2ge 0\ Delta=5^2-4cdot (-2)cdot (-2)=25-16=9\ x_{1}=frac{-5-3}{-4}=frac{-8}{-4}=2\ x_{2}=frac{-5+3}{-4}=frac{-2}{-4}=frac{1}{2}\ \ xin \ \ 4\ frac{x(x-2)}{3}+4=frac{(2x-3)(x-1)-1}{6}+2x setminus cdot 6\ 2x(x-2)+24=(2x-3)(x-1)-1+12x\ 2x^2-4x+24=2x^2-2x-3x+3-1+12x\ -11x=-22\ x=frac{-22}{-11}=2 [/latex]