Question

DAU COROANA calculati media geometricava numerele a =(√5-1)•(1+√10) si b=(√ 10-1)•(1+√5)

Answer 1

a=√5+5√2-1-√10
b=√10+5√2-1-√5
axb=(√5+5√2-1-√10)(√10+5√2-1-√5)=
axb=√50+5√10-√5-5+5√20+50-5√2-5√10-√10-5√2+1+√5-10-5√20+√10+√50
axb=2√50+36-10√2=10√2+36-10√2=36
axb=36
Mg=√axb=√36=6

Answer 2

Deoarece adunarea este comutativa, numerele a si b pot fi 
transformate in felul urmator:

 $a= (\sqrt5-1)(\sqrt{10}+1) \\\;\\ b = (\sqrt{10}-1)(\sqrt5+1)$


$m_g = \sqrt{a\cdot b} =\sqrt{(\sqrt5-1)(\sqrt{10}+1)(\sqrt{10}-1)(\sqrt5+1)}= \\\;\\ =\sqrt{(\sqrt5-1)(\sqrt5+1) (\sqrt{10}-1)(\sqrt{10}+1)}= \sqrt{(5-1)(10-1)} = \sqrt{4\cdot9} \\\;\\ = 2\cdot3 = 6 \\\;\\ .$