3) [latex]sqrt{9 x^{2} -6x+1} =3-|1-3x|[/latex] [latex]sqrt{((1-3x)^2} =3-|1-3x|[/latex] [latex]|1-3x|=3-|1-3x|[/latex] [latex]|1-3x|+|1-3x|=3[/latex] [latex]2|1-3x|=3 /:2[/latex] [latex]|1-3x|=1,5[/latex] [latex]1-3x=1,5 lub 1-3x=-1,5[/latex] [latex]-3x=1,5-1 lub -3x=-1,5-1[/latex] [latex]-3x=0,5 /:(-3) lub -3x=-2,5 /:(-3)[/latex] [latex]x= frac{1}{2} cdot left(- frac{1}{3} ight) lub x=- frac{5}{2} cdot left(- frac{1}{3} ight) [/latex] [latex]x=- frac{1}{6} lub x=- frac{5}{6}[/latex] ==================== 4) [latex]sqrt{ frac{4}{9} x^{2} - frac{4}{3} x+1} =|3-2x|-6[/latex] [latex]sqrt{ frac{1}{9}(4 x^2 -12x+9)} =|3-2x|-6[/latex] [latex] frac{1}{3} sqrt{(3-2x)^2}=|3-2x|-6[/latex] [latex] frac{1}{3} |3-2x|=|3-2x|-6[/latex] [latex] frac{1}{3} |3-2x|-|3-2x|=-6[/latex] [latex]- frac{2}{3} |3-2x|=-6 /:left(- frac{2}{3} ight) [/latex] [latex]|3-2x|=9[/latex] [latex]3-2x=9 lub 3-2x=-9[/latex] [latex]-2x=9-3 lub -2x=-9-3[/latex] [latex]-2x=6 /:(-2) lub -2x=-12 /:(-2)[/latex] [latex]x=-3 lub x=6[/latex] ==================== 5) [latex]sqrt{(4x-1) ^{2} } + sqrt{(4-16x)^2} =10[/latex] [latex]|4x-1|+|4-16x|=10[/latex] [latex]|4x-1|+|-4(4x-1)|=10[/latex] [latex]|4x-1|+4|4x-1|=10[/latex] [latex]5|4x-1|=10 /:5[/latex] [latex]|4x-1|=2[/latex] [latex]4x-1=2 lub 4x-1=-2[/latex] [latex]4x=2+1 lub 4x=-2+1[/latex] [latex]4x=3 /:4 lub 4x=-1 /:4[/latex] [latex]x= frac{3}{4} lub x=- frac{1}{4} [/latex]
