Question

Ajutati-ma si pe mine va rog la acest exercitiu:
Se considera numerele : 
A=$\frac{1}{ \sqrt{3} }$+$\frac{2}{ \sqrt{3} }$+$\frac{ \sqrt{5} }{ \sqrt{15} }$
B=$\frac{ \sqrt{7}+ \sqrt{5} }{ \sqrt{ 21}+ \sqrt{15} }$
a) Calculati A si B rationalizand numitorii
b) Aratati ca $\frac{A+B}{ \sqrt{3} }$∈Q si $\frac{A}{B}$∈Z

Answer 1

A=1/√3 +2/√3 +√5/√15  =
=√3/3 +2√3/3 +√3/3  =
=4√3/3
B=(√7+√5)/(√21+√15)=
=(√7+√5)/[√3(√7+√5)]=
=1/√3 =
=√3/3
(A+B) /√3= (4√3/3+√3/3)/√3=
=(5√3/3 )/√3=5/3=1,(6)  ∈ Q

A/B  =(4√3/3) :√3/3=4√3/3  x 3/√3 = 4 ∈Z