Răspuns:
a)
[tex] a=\sqrt{2}+1, b=\sqrt{2}-1,\; a+b=2\sqrt{2},\;a-b=2[/tex]
[tex] (a+b)^2 = (2\sqrt{2})^2 = 2^2 (\sqrt{2})^2 = 4\cdot 2 = 8 [/tex]
[tex] (a-b)^3 = 2^3 = 8 = (a+b)^2 [/tex]
b)
media geometrica [tex] = \sqrt{ab} = \sqrt{(\sqrt 2 +1)(\sqrt 2 -1)} = \sqrt{ (\sqrt 2)^2 -1 ^2}= \sqrt{2-1}=\sqrt 1 = 1 [/tex]
