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[latex]a=frac{(480^3:240^3)cdotleft[left(1frac{1}{2} ight) ^{20}:left(1frac{1}{2} ight) ^{17} ight] }{3sqrt3}[/latex] [latex]a=frac{(480:240)^3cdotleft(1frac{1}{2} ight) ^{3} }{3sqrt3}[/latex] [latex]a=frac{2^3cdotleft(frac{3}{2} ight) ^{3} }{3sqrt3}[/latex] [latex]a=frac{8cdotfrac{27}{8}}{3sqrt3}[/latex] [latex]a=frac{27}{3sqrt3}[/latex] [latex]a=frac{9}{sqrt3}[/latex] [latex]a=frac{9sqrt3}{3}[/latex] [latex]a=3sqrt3[/latex] [latex](2a + 1)(2a - 1) - frac{1}{2} (a-3)^2- frac{1}{2}a(7+5a)=[/latex] [latex]4a^2-1 -0,5(a^2-6a+9)-3,5a-2,5a^2 =[/latex] [latex]4a^2-1 -0,5a^2+3a-4,5 -3,5a-2,5a^2 =[/latex] [latex]a^2-0,5a-5,5[/latex] [latex](3sqrt3)^2-0,5cdot 3sqrt3-5,5=27-1,5 sqrt{3} -5,5=[/latex] [latex]-1,5 sqrt{3}+21,5[/latex] ===================== [latex]a=- frac{3}{4}[/latex] [latex]x=-1 frac{1}{2}[/latex] [latex]2aleft( frac{1}{2} a+ frac{1}{4} x ight) -3xleft(frac{1}{6} a+ frac{1}{9} x ight) =[/latex] [latex]a^2+ frac{1}{2} ax-frac{1}{2} ax-frac{1}{3} x^2=[/latex] [latex]a^2-frac{1}{3} x^2[/latex] [latex]left(- frac{3}{4} ight)^2- frac{1}{3}cdot left(-1 frac{1}{2} ight)^2=frac{9}{16}- frac{1}{3}cdot left(-frac{3}{2} ight)^2=[/latex] [latex]frac{9}{16}- frac{1}{3}cdot frac{9}{4}=frac{9}{16}- frac{9}{12}=frac{27}{48}- frac{36}{48}=-frac{9}{48}=- frac{3}{16}[/latex] ===================== a) [latex]a = -2[/latex] [latex]b = -3[/latex] [latex]a^3 - 3a^2b - b^3 + 3ab^2=(a-b)^3[/latex] [latex](-2-3)^3=(-5)^3=-125[/latex] b) [latex]a = 0,5[/latex] [latex]b = 0,3[/latex] [latex]a^3 + 2a^2 - 2ab^2 - 4b^2[/latex] [latex]0,5^3 + 2cdot 0,5^2 - 2cdot 0,5cdot 0,3^2 - 4cdot 0,3^2=[/latex] [latex]0,125 + 2cdot 0,25 - 0,09 - 4cdot 0,09=[/latex] [latex]0,125 + 0,5 - 0,09 - 0,36=0,175[/latex] c) [latex]a=1frac{1}{2}[/latex] [latex]b=frac{2}{3}[/latex] [latex]frac{a^2+ab}{ab-b^2}-frac{a}{b}=frac{a^2+ab}{b(a-b)}-frac{a}{b}=[/latex] [latex]frac{a^2+ab}{b(a-b)}-frac{a(a-b)}{b(a-b)}=[/latex] [latex]frac{a^2+ab-a^2+ab}{b(a-b)}=frac{2ab}{b(a-b)}= frac{2a}{a-b}[/latex] [latex]frac{2cdot 1frac{1}{2}}{1frac{1}{2}-frac{2}{3}}=frac{3}{1frac{3}{6}-frac{4}{6}}=frac{3}{frac{9}{6}-frac{4}{6}}=[/latex] [latex]frac{3}{frac{5}{6}}= frac{18}{5}=3 frac{3}{5}[/latex] ===================== [latex]b=frac{left(-frac{1}{2} ight) ^2-0,8:frac{4}{5}}{-2}+frac{1}{8}[/latex] [latex]b=frac{frac{1}{4}-0,8:0,8}{-2}+frac{1}{8}[/latex] [latex]b=frac{frac{1}{4}-1}{-2}+frac{1}{8}[/latex] [latex]b=frac{-frac{3}{4}}{-2}+frac{1}{8}[/latex] [latex]b=frac{3}{8}+frac{1}{8}[/latex] [latex]b=frac{4}{8}[/latex] [latex]b=0,5[/latex] [latex](sqrt3-sqrt{2b})(3+2b)(sqrt3+sqrt{2b})=[/latex] [latex](3+2b)(3-2b)=9-4b^2[/latex] [latex]9-4cdot 0,5^2=9-4cdot 0,25=9-1=8[/latex]