g) [latex]x^3=frac{1}{2}x^2+2x-1 / cdot 2[/latex] [latex]2x^3=x^2+4x-2[/latex] [latex]2x^3-x^2-4x+2=0[/latex] [latex]x^2(2x-1)-2(2x-1)=0[/latex] [latex](2x-1)(x^2-2)=0[/latex] [latex](2x-1)(x-sqrt{2})(x+sqrt{2})=0[/latex] [latex]2x-1=0 lub x-sqrt{2}=0 lub x+sqrt{2}=0[/latex] [latex]2x=1 /:2 lub x=sqrt{2} lub x=-sqrt{2}[/latex] [latex]x= frac{1}{2}[/latex] [latex]x in left{-sqrt{2}; frac{1}{2} ;sqrt{2} ight}[/latex] h) [latex]frac{x^3}{2}+frac{3}{4}x^2=3+2x / cdot 4[/latex] [latex]2x^3+3x^2=4(3+2x)[/latex] [latex]2x^3+3x^2-4(3+2x)=0[/latex] [latex]x^2(2x+3)-4(2x+3)=0[/latex] [latex](2x+3)(x^2-4)=0[/latex] [latex](2x+3)(x-2)(x+2)=0[/latex] [latex]2x+3=0 lub x-2=0 lub x+2=0[/latex] [latex]2x=-3 /:2 lub x=2 lub x=-2[/latex] [latex]x=-1,5[/latex] [latex]x in left{-2;-1,5 ;2 ight}[/latex] i) [latex]frac{1}{4}-frac{1}{2}x=frac{1}{2}x^2-x^3 / cdot 4[/latex] [latex]1-2x=2x^2-4x^3[/latex] [latex]1-2x-2x^2+4x^3=0[/latex] [latex](1-2x)-2x^2(1-2x)=0[/latex] [latex](1-2x)(1-2x^2)=0[/latex] [latex](2x-1)(2x^2-1)=0[/latex] [latex](2x-1)( sqrt{2} x-1)( sqrt{2} x+1)=0[/latex] [latex]2x-1=0 lub sqrt{2} x-1=0 lub sqrt{2}x+1=0[/latex] [latex]2x=1 /:2 lub sqrt{2} x=1 /:sqrt2 lub sqrt{2}x=-1 /:sqrt2[/latex] [latex]x=frac{1}{2} lub x= frac{sqrt2}{2} lub x=-frac{sqrt2}{2}[/latex] [latex]x in left{frac{sqrt2}{2}; frac{1}{2} ;frac{sqrt2}{2} ight}[/latex]
