Question

Fie a= √125 - √5. iar b=√(4√5 - 8)²

Answer 1

a = √125  - √5 = √25·√5  - √5 = 5√5  - √5 = 4√5 
b = I 4√5 - 8I  =  numar pozitiv   = 4√5 - 8
med. aritm = [ a +b ] /2 = [ 4√5 + 4√5 - 8 ] / 2 = [ 8 √5 - 8 ] / 2 = 
= 4 ( √5 -1 ) 

Answer 2

$\bold{M_a= \frac{a+b}{2}} \\ a= \sqrt{125} - \sqrt{5}= \sqrt{25} \cdot \sqrt{5}- \sqrt{5}=5 \cdot \sqrt{5} - \sqrt{5} =\bold{4 \sqrt5} ; \\ b= \sqrt{(4 \sqrt{5}-8)^2 }=\bold{4 \sqrt5-8} ; \\ \Rightarrow M_a= \frac{4\sqrt5+4\sqrt5-8}{2} = \frac{2 \cdot 4\sqrt5-8}{2}=\frac{8\sqrt5-8}{2}= \boxed{4\sqrt5-4}.$