Question

Fie numerele a=radical din 5+2 radical din 6 si b=radical din 5-2 radical din 6.Calculati:a)media aritmetica a celor doua numere;b) media geometrica a numerelor a si b

Answer 1

formula radicalilor compusi

a=√(5+2√6)=√(5+√24)=√(5+√25-24)/2+√(5-√25-24)/2=√(5+√1)/2+√(5-√1)/2=
=√6/2+√4/2=√3+√2
b=√(5-2√6)=√(5-√24)=√(5+√25-24)/2-√(5-√25-24)/2=√(5+√1)/2-√(5-√1)/2=
=√6/2-√4/2=√3-√2
ma=(√3+√2+√3-√2)/2=2√3/2=√3
mg=√(√3+√2)(√3-√2)=√(3-2)=√1=1


sau
a=√(5+2√6)=√(3+2√3×√2+2)=√(√3+√2)²=√3+√2
b=√(5-2√6)=√(3-2√3×√2+2)=√(√3-√2)²=√3-√2
ma=(√3+√2+√3-√2)/2=2√3/2=√3
mg=√(√3+√2)(√3-√2)=√(3-2)=√1=1