Răspuns:
[tex]a) \: a = 11 \sqrt{5} - 5 \sqrt{5} + 8 \sqrt{5} - 6 \sqrt{5} = 8 \sqrt{5} \\ b = 10 \sqrt{5} - 12 \sqrt{5} + 3 \sqrt{5} - 4 \sqrt{5} = - 3 \sqrt{5} \\ \frac{a + 2b}{2a - b} = \frac{8 \sqrt{5} + 2 \times ( - 3 \sqrt{5}) }{2 \times 8 \sqrt{5} - ( - 3 \sqrt{5} )} = \frac{8 \sqrt{5} - 6 \sqrt{5} }{10 \sqrt{5} + 3 \sqrt{5} } = \frac{2 \sqrt{5} }{13 \sqrt{5} } = \frac{2}{13} apartine \: q \: mare[/tex]
[tex]b) \: a = 2 \sqrt{3} - 3 \sqrt{3} + 5 \sqrt{3} + \sqrt{3} = 5 \sqrt{3} \\ b = 13 \sqrt{3} - 9 \sqrt{3} - 2 \sqrt{3} + 3 \sqrt{3} = 5 \sqrt{3} \\ \frac{a + 2b}{2a - b} = \frac{5 \sqrt{3} + 2 \times 5 \sqrt{3} }{2 \times 5 \sqrt{3} - 5 \sqrt{3} } = \frac{5 \sqrt{3} + 10 \sqrt{3} }{10 \sqrt{3} - 5 \sqrt{3} } = \frac{15 \sqrt{3} }{5 \sqrt{3} } = \frac{15}{5} = 3 \: apartine \: q \: mare[/tex]
[tex]c) \: a = 7 \sqrt{11} + 4 \sqrt{11} - 9 \sqrt{11} + \sqrt{11} = 3 \sqrt{11} \\ b = 26 \sqrt{11} - 10 \sqrt{11} - 7 \sqrt{11} - 6 \sqrt{11} = 3 \sqrt{11} \\ \frac{a + 2b}{2a - b} = \frac{3 \sqrt{11} + 2 \times 3 \sqrt{11} }{2 \times 3 \sqrt{11} - 3 \sqrt{11} } = \frac{3 \sqrt{11} + 6 \sqrt{11} }{6 \sqrt{11} - 3 \sqrt{11} } = \frac{9 \sqrt{11} }{3 \sqrt{11} } = \frac{9}{3} = 3 \: apartine \: q \: mare[/tex]
[tex]d) \: a = - 6 \sqrt{6} - 5 \sqrt{6} + 7 \sqrt{6} + 2 \sqrt{6} = - 2 \sqrt{6} \\ b = 4 \sqrt{6} - 10 \sqrt{6} + 3 \sqrt{6} + 2 \sqrt{6} = - \sqrt{6} \\ \frac{a + 2b}{2a - b} = \frac{ - 2 \sqrt{6} + 2 \times ( - \sqrt{6}) }{2 \times ( - 2 \sqrt{6}) - ( - \sqrt{6} ) } = \frac{ - 2 \sqrt{6} - 2 \sqrt{6} }{ - 4 \sqrt{6} + \sqrt{6} } = \frac{ - 4 \sqrt{6} }{ - 3 \sqrt{6} } = \frac{ - 4}{ - 3} = \frac{4}{3} apartine \: q \: mare[/tex]