[tex]\sf ^{1-\sqrt2)}\frac{1}{1+ \sqrt{2} } +^{\sqrt2-\sqrt3)} \frac{1}{ \sqrt{2}+\sqrt{3} } + ^{\sqrt3-2)}\frac{1}{ \sqrt{3}+2 }= \\ \\ \frac{1-\sqrt2}{(1-\sqrt2)(1+\sqrt2)}+\frac{\sqrt2-\sqrt3}{(\sqrt2-\sqrt3)(\sqrt2+\sqrt3)}+\frac{\sqrt3-2}{(\sqrt3-2)(\sqrt3+2)}= \\ \\ \frac{1-\sqrt2}{1-2}+\frac{\sqrt2-\sqrt3}{2-3}+\frac{\sqrt3-2}{3-4}= \\ \\ -1+\sqrt2-\sqrt2+\sqrt3-\sqrt3+2=1 \\ \\ 1 \in{N[/tex]
Cu drag, Amalia Georgiana Monica Andreea Florica de la Cluj!
