[latex]a) x+1=frac{2-2x}{x-1}; D:x eq1\\x+1=frac{-2(x-1)}{x-1}\\x+1=-2\\x=-2-1\\x=-3[/latex] ========================================================== [latex]b) frac{2x-2}{x+2}=frac{x}{x-1}; D:x eq-2 wedge x eq1\\(2x-2)(x-1)=x(x+2)\\2x^2-2x-2x+2=x^2+2x\\2x^2-x^2-4x-2x+2=0\\x^2-6x+2=0\\Delta=(-6)^2-4cdot1cdot2=36-8=28; sqrtDelta=sqrt{28}=sqrt{4cdot7}=2sqrt7\\x_1=frac{6-2sqrt7}{2cdot1}=3-sqrt7; x_2=frac{6+2sqrt7}{2cdot1}=3+sqrt7[/latex] =========================================================== [latex]c) frac{2}{5x+10}=frac{-3}{x^2-4}; D:x eq-2 wedge x eq2\\2(x^2-4)=-3(5x+10)\\2x^2-8=-15x-30\\2x^2+15x-8+30=0\\2x^2+15x+22=0\\Delta=15^2-4cdot2cdot22=225-176=49; sqrtDelta=sqrt{49}=7\\x_1=frac{-15-7}{2cdot2}=frac{-22}{4}=-5,5; x_2=frac{-15+7}{2cdot2}=frac{-8}{4}=-2 eq D[/latex]
a) /* (x-1) x(x-1)+x-1=2-2x x²-x+x-1=2-2x x²+2x-3=0 Δ=4+12=16 x1=[-2-4]/2=-3 x2=[-2+4]/2=1 D: x∈R/[1] b) x(x+2)=(2x-2)(x-1) x²+2x=2x²-2x-2x+2 x²-6x+2=0 Δ=36-8=28 x1=[6-2√7]/2=3-√7 x2=[=3+√7 D: x∈R /[-2,1] c) 2(x²-4)=-3(5x+10) 2x²-8=-15x-30 2x²+15x+22=0 Δ=225-176=49 x1=[-15-7]/4=-22/4=-11/2 x2=[-15+7]/4=-2 d: X∈r/[-2,2,]
Rozwiąż Równania: a) [latex] frac{5}{x-10}= frac{-3}{1-2x} [/latex] b) [latex] frac{6}{9x+2}= frac{4}{6x+1} [/latex] c) [latex] frac{x+5}{2} = frac{10+2x}{4} [/latex]...
Rozwiąż równania: [latex]frac{2}{5x+10} = frac{-3}{x^{2}-4 } [/latex] [latex] frac{2x+5}{ x^{2}-1 } = frac{1}{x+1 } [/latex] [latex] frac{6}{x} -1= frac{2}{x-1} [/latex] [latex] frac{2x+1}{ x^{2}-9 } - frac{3}{x-3} =0[/latex]...
rozwiąż równania: 1.[latex]frac{x+7}{x-3}=2x-4 [/latex] 2.[latex]frac{x+3}{x^{2}+4x-5} + frac{x}{x-1}[/latex] 3.[latex]frac{2x^{2}-2x}{x^{2}+x-6}cdot frac{x^{2}-9}{x-1}[/latex] ...
Rozwiąż równania: 1. [latex] frac{4}{x} = frac{3}{2+x} [/latex] 2. [latex] frac{2}{x+2} - frac{1}{x-3}= 0 [/latex]...
Zredukuj równania do prostszej postaci a następnie rozwiąż i znajdź niewiadomą: 13k-9-10k=0 [latex] frac{1}{5}y+[latex] frac{4}{5} [/latex]y=10 [latex] frac{4}{9} [/+[latex] frac{4}{5} [/latex]tex]k+[latex] frac{5}{9} [/latex]k=10...
