Question

Fie numerele:
a=$\sqrt{5+2 \sqrt{6}}$
b=$\sqrt{5-2 \sqrt{6}}$
a)Calculati media aritmetica a numerelor a si b
b)Calculati media geometrica a numerelor a si b

Answer 1

a) $ma= \frac{a+b}{2} = \frac{ \sqrt{5+2 \sqrt{6} }+ \sqrt{5-2 \sqrt{6} } }{2}$

b)$mg= \sqrt{ab} = \sqrt{ \sqrt{5 +2 \sqrt{6} } \sqrt{5- 2\sqrt{6} } } = \sqrt{( \sqrt{25-24} )}= \sqrt{ \sqrt{1} } =1$