Răspuns:
x = -2 ∈ Z
Explicație pas cu pas:
[tex]x = \sqrt{3} (\frac{\sqrt{3} }{3} + \frac{5}{2\sqrt{3} } ) - (\frac{24 - 15}{10\sqrt{3} } ) *\sqrt{27} - (\frac{4\sqrt{3}+10\sqrt{3} }{5} )*\frac{1}{\sqrt{3} }[/tex]
[tex]x = \sqrt{3} (\frac{\sqrt{3} }{3} + \frac{5\sqrt{3} }{6} ) - \frac{9}{10\sqrt{3} } *3\sqrt{3} - \frac{14\sqrt{3} }{5} * \frac{1}{\sqrt{3} }[/tex]
[tex]x = \sqrt{3} * \frac{2\sqrt{3}+5\sqrt{3} }{6} - \frac{27}{10} - \frac{14}{5}[/tex]
[tex]x = \sqrt{3} * \frac{7\sqrt{3} }{6} - \frac{27}{10} - \frac{28}{10}[/tex]
[tex]x = \frac{21}{6} - \frac{55}{10}[/tex]
[tex]x = \frac{21*5 - 55*3}{30}[/tex]
[tex]x = \frac{105 - 165}{30} = \frac{-60}{30}[/tex]
x = -2 - am demonstrat că x este număr întreg.
