Zad.1 [latex]a) =sqrt{frac{25}{9}}-(-frac{5}{2})^2=frac{5}{3}-frac{25}{4} = frac{20}{12}-frac{75}{12}=-frac{55}{12}=-4frac{7}{12}\ \ b) = [frac{6^{3+4}}{6^{13-7}}]^{-1}=[frac{6^7}{6^{6}}]^{-1}=(6^{7-6})^{-1}=(6^{1})^{-1}=6^{-1}=frac{1}{6}\ \ c) =frac{2cdot 4sqrt{2}-6sqrt{2}}{2sqrt{2}}=frac{8sqrt{2}-6sqrt{2}}{2sqrt{2}}frac{2sqrt{2}}{2sqrt{2}}=1\ \ e) = frac{(-1)^{9}cdot 5^9cdot 5^9}{5^{18}} = frac{-(5^{9+9})}{5^{18}} = frac{-(5^{18})}{5^{18}}=-1\ \ [/latex] [latex]f) = 10^6cdot 10^{-7}cdot (-1)^2 cdot (10^{-1})^2 =10^{6+(-7)+(-2)}=10^{-3}=0,001[/latex] [latex]g) = (1,25cdot 40)^3= 50^3= 125000[/latex] Zad.2 [latex]a)\ egin{cases}8x-6y=10\7x+y=5 --> y=5-7xend{cases}\ \ 8x-6(5-7x)=10\ 8x-30+42x=10\ 50x=40\ x=frac{4}{5}\ \ y=5-7cdot frac{4}{5}=5-frac{28}{5}=-frac{3}{5}\ \ egin{cases}x=frac{4}{5}\y=-frac{3}{5}end{cases} [/latex] [latex]b)\ egin{cases}12x-7y=-16\x-3y=-69 --> x=3y-69end{cases}\ \ 12(3y-69)-7y=-16\ 36y-828-7y=-16\ 29y=812\ y=28\ \ x=3y-69=84-69=15\ \ egin{cases}x=15\y=28end{cases}[/latex] [latex]c)\ egin{cases}4(x-2)-(y-2)=1\10x-2y=18end{cases}\ \ egin{cases}4x-8-y+2=1 --> y=4x-7\10x-2y=18end{cases}\ \ 10x-2(4x-7)=18\ 10x-8x+14=18\ 2x=4\ x=2\ \ y=4x-7=8-7=1\ \ egin{cases}x=2\y=1end{cases} [/latex] d) niepełny zapis najprostsza postać: [latex]a) =x\ \ b) =-(7y+40)\ \ c) =-18a-36c+27\ \ d) =19\ \ e) =-15x-13y=-(15x+13y)\ \ f) =3x^2-11a\ \ g) =-11a-4=-(11a+4)\ \ h) =12-1=11[/latex]
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