Răspuns:
a+b+c=10
Explicație pas cu pas:
[tex]a = 7 - 5\sqrt{10}\\\\b = 2\sqrt{5} + 9\sqrt{10} - 3\\\\c = 6-4\sqrt{10} - 2\sqrt{5}\\\\a+b+c = (7-5\sqrt{10}) + (2\sqrt{5} + 9\sqrt{10} - 3) + (6 - 4\sqrt{10} - 2\sqrt{5}) = 7 - 5\sqrt{10} + 2\sqrt{5} + 9\sqrt{10} - 3 + 6 - 4\sqrt{10} - 2\sqrt{5}\\\\ 7 - 3 + 6 = 10\\\\ -5\sqrt{10} + 9\sqrt{10} - 4\sqrt{10} = \sqrt{10}(-5+9-4) = \sqrt{10}\cdot 0 = 0\\\\ 2\sqrt{5} - 2\sqrt{5} = \sqrt{5}(2-2) = \sqrt{5}\cdot 0 = 0\\\\\implies a+b+c = 10 + 0 + 0 = 10[/tex]
