Question

Se consideră numerele a = 4/$\sqrt(6 + 2 \sqrt5 )$ si b = $\sqrt5 - 1$
Calculati media geometrica a celor 2 numere.

Answer 1

radical compus
√(6+2√5)=√(6+√20)=√[6+√(36-20)]/2+√[6-√(36-20)]/2=
=√(6+√16)/2+√(6-√16)/2=√(6+4)/2+√(6-4)/2=√10/2+√2/2=√5+1

a=4/√(6+2√5) =4/(√5+1)
b=√5+1
mg=√a×b=√4/(√5+1)×(√5+1)=√4=2