Răspuns:
8
Explicație pas cu pas:
Metoda 1 (prin depistarea patratelor perfecte):
[tex]a=\sqrt{3+2\sqrt2}+\sqrt{3-2\sqrt2}\\a=\sqrt{(1+\sqrt2)^2}+\sqrt{(1-\sqrt2)^2}\\a=|1+\sqrt2|+|1-\sqrt2|\\a=1+\sqrt2+\sqrt2-1\\a=2\sqrt2\\a^2=8[/tex]
Metoda 2 (prin calcul direct):
[tex]a=\sqrt{3+2\sqrt2}+\sqrt{3-2\sqrt2}\\a^2=(\sqrt{3+2\sqrt2}+\sqrt{3-2\sqrt2})^2\\a^2=3+2\sqrt2+3-2\sqrt2+2*\sqrt{3+2\sqrt2}*\sqrt{3-2\sqrt2}\\a^2=6+2*\sqrt{(3+2\sqrt2)*(3-2\sqrt2)}\\a^2=6+2*\sqrt{9-8}\\a^2=6+2\\a^2=8[/tex]
