[latex]a=0,3*log_{sqrt{2}}2^{3frac{1}{3}}[/latex] = [latex]= frac{3}{10} * log_{sqrt{2}}((sqrt{2})^{2})^{3frac{1}{3}}[/latex] = = [latex]frac{3}{10} * log_{sqrt{2}}(sqrt{2})^{6frac{2}{3}}[/latex] = =[latex]frac{3}{10} * 6 frac{2}{3} * log_{sqrt{2}} (sqrt{2}) = frac {3}{10} * frac{20}{3} * 1 = 2[/latex] [latex]b= frac{6 * sqrt[4]{2} - 2 frac{5}{4}}{64^{0,125}} = frac{3 * 2 * 2^{frac{1}{4}} - 2 frac{5}{4}}{((2)^{6)^{frac{1}{8}}}} = frac{3 * 2^{ frac{5}{4}} - 2 frac{5}{4}}{2^{frac{3}{4}}}[/latex] w zadaniu prawdopodobnie jest błąd i moim zdaniem powinno być: [latex]b= frac{6 * sqrt[4]{2} - 2^{frac{5}{4}}}{64^{0,125}} [/latex] zamiast wymienionego w treści zadania wtedy b= [latex]frac{3 * 2^{ frac{5}{4}} - 2^{frac{5}{4}}}{2^{frac{3}{4}}} = frac{2^{frac{5}{4}}(3-1)}{2^{frac{3}{4}}} = 2^{frac{5}{4} - frac{3}{4}} * 2 = 2^{frac{1}{2}} *2 = 2^{frac{3}{2}}= sqrt[2]{2^3}= [/latex] [latex]sqrt{8}[/latex] a=2 [latex]b=2 sqrt{2}[/latex] [latex](a - 0,5 b)^{2} = ( 2 - 0,5 * 2 sqrt{2})^{2} = (2 - sqrt{2})^{2} = 4 - 4 sqrt{2} + 2 = 6 - 4 sqrt{2}[/latex]
