Опростяване на израз с корени

[atnast]

Опростете израза [tex]\sqrt{12-\sqrt{24}+\sqrt{39}-\sqrt{104}} -\sqrt{12+\sqrt{24}+\sqrt{39}+\sqrt{104}}[/tex].

[Xixibg]

Нека[tex]A=\sqrt{12-\sqrt{24}+\sqrt{39}-\sqrt{104}} -\sqrt{12+\sqrt{24}+\sqrt{39}+\sqrt{104}} ; =>A<0[/tex]
[tex]A^2=24+2\sqrt{39}-2\sqrt{55+8\sqrt{39}}=24+2\sqrt{39}-2\sqrt{(4+\sqrt{39})^2}[/tex]
[tex]=24+2\sqrt{39}-2(4+\sqrt{39})=24+2\sqrt{39}-8-2\sqrt{39}=16[/tex]
[tex]=>A=-\sqrt{16}=-4[/tex]