1. 4-x(x-1)=6+2(x-3) 4-x²+x=6+2x-6 -x²+x-2x+4=0 -x²-x+4=0 x²+x-4=0 Δ=1-4·(-4)=1+16=17 √Δ=√17 [latex]x_1=frac{-1+sqrt{17}}{2}[/latex] [latex]x_2=frac{-1-sqrt{17}}{2}[/latex] 2. 2x²>3x+5 2x²-3x-5>0 Δ=(-3)²-4·2·(-5)=9+40=49 √Δ=7 [latex]x_1=frac{3+7}{4}=frac{5}{2}[/latex] [latex]x_2=frac{3-7}{4}=frac{-4}{4}=-1[/latex] odp. [latex]x in (-infty,-1) cup (frac{5}{2},+infty)[/latex] 3. (x-6)(x+2)=2(4-2,5x) x²+2x-6x-12=8-5x x²-4x+5x-12-8=0 x²+x-20=0 Δ=1²-4·1·(-20)=1+80=81 √Δ=9 [latex]x_1=frac{-1+9}{2}=4[/latex] [latex]x_2=frac{-1-9}{2}=-5[/latex] 4. 2x+8x²>3 8x²+2x-3>0 Δ=4+96=100 √Δ=10 [latex]x_1=frac{-2+10}{16}=frac{8}{16}=frac{1}{2}[/latex] [latex]x_2=frac{-2-10}{16}=-frac{3}{4}[/latex] odp. [latex]x in (-infty,-frac{3}{4}) cup (frac{1}{2},+infty)[/latex] 5. (4-3x)²=16-9x² 16-24x+9x²=16-9x² 18x²-24x=0:6 3x²-4x=0 x(3x-4)=0 x=0 ∨ 3x=4 x=0 ∨ x=[latex]frac{4}{3}[/latex]
