Matematyka

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[latex]19.\\3*(sqrt[4]{3})^{12} = 3*(3^{frac{1}{4}})^{12}=3*3^{3} = 3^{4} = 81[/latex] [latex]20.\\|1-3*4frac{1}{2}|= |3*4frac{1}2}-1| = 3*frac{9}{2}-1 = frac{27}{2}-frac{2}{2}=frac{25}{2} = 12frac{1}{2}[/latex] [latex]21.\\x extless -3\\x in (-infty;-3)[/latex] [latex]22.\\x(x^{2}-1)= 0\\x(x+1)(x-1) = 0\\x = 0 vee x = -1 vee x = 1\\x inlbrace-1;0;1 brace[/latex] [latex]23.\\delta =frac{|4-3,75|}{3,75}*100\% = frac{0,25}{3,75}*100\% = 6,(6)\%[/latex] [latex]24.\\sqrt[4]{7-sqrt{33}}*sqrt[4]{7+sqrt{33}} = sqrt[4]{(7-sqrt{33})7+sqrt{33})} = sqrt[4]{49-33}=sqrt[4]{16} = 2[/latex] [latex]25.\\4n+3, nin N[/latex] [latex]26.\\x = frac{32^{10}*(frac{1}{4})^{19}}{8^{-1}}= frac{(2^{5})^{10}*(2^{-2})^{19}}{(2^{3})^{-1}}=frac{2^{50}*2^{-38}}{2^{-3}} = frac{2^{12}}{2^{-3}} = 2^{15}\\y = 2^{18}-5*2^{15}-2^{16}=2^{15}(2^{3}-5-2) = 2^{15}(8-5-2)= 2^{15}, zatem\\x = y[/latex] [latex]27.\\(2x-1)(x^{2}+10x+25) = 0\\(2x-1)(x+5)^{2} = 0\\x = frac{1}{2} vee x = -5\\x = lbrace-5;frac{1}{2} brace[/latex] [latex]28.\\(5-2x)^{2}-5(x-2)(x+2) = 25-20x+4x^{2}-5(x^{2}-4)=\\=25-20x+4x^{2}-5x^{2}+20 = -x^{2}-20x+45[/latex]

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Matematyka