Zad1. a) [latex]frac{2-4sqrt3}{1+2sqrt3}=frac{2(1-2sqrt3)}{1+2sqrt3}=\=frac{2(1-2sqrt3) cdot (1-2sqrt3)}{(1+2sqrt3) cdot (1-2sqrt3)}=frac{2(1-sqrt3)^2}{1-12}=frac{2(1-2sqrt3+3)}{-11}=\=-frac{2(4-2sqrt3)}{11}=-frac{4}{11}(2-sqrt3)[/latex] b) [latex]frac{1}{sqrt2-1}=frac{1 cdot (sqrt2+1)}{(sqrt2-1) cdot (sqrt2+1)}=\=frac{sqrt2+1}{2-1}=sqrt{2}+1[/latex] Zad2. [latex]egin{cases}-2x-6x+1=5x-4(x+2y)\ y-2x+2=frac{3x-y}{2}end{cases}[/latex] [latex]egin{cases}-8x+1=5x-4x-8y\ 2y-4x+4=3x-yend{cases}[/latex] [latex]egin{cases}-8x+1=x-8y \ 2y-4x-3x+y=-4end{cases}[/latex] [latex]egin{cases}-8x-x+8y=-1 \ -7x+3y=-4end{cases}[/latex] [latex]egin{cases}-9x+8y=-1 /cdot 3 \ -7x+3y=-4 /cdot (-8)end{cases}[/latex] [latex]underline{egin{cases}-27x+24y=-3\ 56x-24y=32end{cases}}[/latex] [latex]+[/latex] [latex]-27x+56x+24y-24y=-3+32[/latex] [latex]29x=29[/latex] [latex]x=frac{29}{29}[/latex] [latex]x=1[/latex] [latex]-9x+8y=-1[/latex] [latex](-9) cdot 1+8y=-1[/latex] [latex]-9+8y=-1[/latex] [latex]8y=-1+9[/latex] [latex]8y=8[/latex] [latex]y=1[/latex] Odp. [latex]egin{cases} x=1 \ y=1 end{cases}[/latex] Pozdrawiam.
Usuń niewymierność z mianownika ułamka a) [latex]frac{2-4sqrt{3}}{1+2sqrt{3}}[/latex] b) [latex]frac{1}{sqrt{2} -1}[/latex] Oblicz układ równań [latex]left{ {{-2x-6x+1=5x-4(x+2y)}atop{y-2x+2=frac{3x-y}{2}[/latex]
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