Question

Calculati media geometrica a numerelor a=4 +√80 si b=4(√5-1)
b)Aratati ca numarul √6-2 supra √6 +2 : (√3 -√2) supra 2 este numar natural

Answer 1

a)a=4+√80=4+4√5
b=4(√5-1)=4√5-4
Mg=√ab=√(4+4√5)(4√5-4)=√(16√5-16+16·5-16√5)=
=√-16+80=√64
Mg=8
b) (√6-2)/√6+2):(√3-√2)/2=(√6-2)/(√6+2)·2/(√3-√2)=
(√6-2)/√6+2)=rationalizam=(√6-2)(√6-2)/(6-4√6+4)=(10-4√6)/2=2(5-2√6)/2=5-2√6
2/(√3-√2)=rationalizam=2(√3+√2)/3-2=2(√3+√2)
⇒(5-2√6)·(2√3+2√2)=10√3-10√2-4√18-4√12=10√3-10√2-4·3√2-4·2√3=
10√3-8√3-10√2-12√2=2√3-22√2=2(√3-11√2)