Question

verificati daca m= (2/radical din 2 - 3/ radical din 3) (radical din 2 + radical din 3) este nr. intreg

Answer 1

   
[tex]\displaystyle \\ m= \Big(\frac{2}{\sqrt{2} }-\frac{3}{\sqrt{3}}\Big)\Big(\sqrt{2}+\sqrt{3}\Big)= \\ \\ =\Big(\frac{2\times \sqrt{2} }{\sqrt{2} \times \sqrt{2}}-\frac{3\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}\Big)\Big(\sqrt{2}+\sqrt{3}\Big)= \\ \\ =\Big(\frac{2\times \sqrt{2} }{2}-\frac{3\times \sqrt{3}}{3}}\Big)\Big(\sqrt{2}+\sqrt{3}\Big)= \\ \\ =\Big(\sqrt{2} -\sqrt{3}}\Big)\Big(\sqrt{2}+\sqrt{3}\Big)= \\ \\ =(\sqrt{2})^2 - (\sqrt{3})^2 = 2-3 = \boxed{-1 \in Z } [/tex]