log(2x^{2} −4x)≥log(x+3) Dziedzina: 2x^{2}−4x>0 2x(x−2)>0 x∈(−∞,0)∪(2,∞) x+3>0 x∈(−3,∞) Dziedzina to część wspólna przedziałów D=(−3,0)∪(2,+∞) 2x^{2}−4x≥x+3 2x^{2}−4x−x−3≥0 2x^{2}−5x−3≥0 δ=49 δ√=7 x1=3 x2=[latex] frac{-1}{2} [/latex] x∈(−∞,[latex] frac{-1}{2} [/latex])∪(3,∞) odp. x∈([latex] frac{-1}{2} [/latex],0)∪(3,∞)
[latex]log(2x^{2}-4x) geq log(x + 3)[/latex] -------------------------- Dziedzina: [latex]egin{cases}2x^2-4x>0\ x+3>0end{cases}[/latex] [latex]egin{cases}2x(x-2)>0\ x>-3end{cases}[/latex] [latex]egin{cases}xin(-infty;0)cup (2;+ infty )\ x>-3end{cases}[/latex] [latex]xin(-3;0)cup (2;+infty)[/latex] -------------------------- [latex]2x^{2}-4x geq x+3[/latex] [latex]2x^2-4x-x-3 geq 0[/latex] [latex]2x^2-5x-3 ge 0[/latex] [latex]Delta=(-5)^2-4cdot 2cdot (-3)=25+24=49[/latex] [latex]sqrt{Delta}= sqrt{49}=7[/latex] [latex]x_1=frac{5-7}{4}=-frac{1}{2}[/latex] [latex]x_2=frac{5+7}{4}=3[/latex] [latex]xin (- infty ;- frac{1}{2}>cup <3;+ infty )[/latex] Po uwzględnieniu dziedziny [latex]xin (-3; -frac{1}{2}>cup <3;+ infty)[/latex]
