Question

Exercitiul 10 va rog mult

Answer 1

1)A=√3/3+2√3/3+√15•√5/15= 3√3/3+√75/15= √3+√75/15= (15√3+√25•√3)/15=√3(15+√25)/15=√3(15+5)/15=√3•20/15 =4√3/3
B=(√7+√5)(√21-√15)/(√21+√15)(√21-√15)=(√7•√21+√7•√15-√5•√21-√5•√15)/(21-15)= (7√3+√105+√105-5√3)/6= (3√3+2√105)/6=√3(3+2√35)/6.
2)(A+B)/√3=[4√3/3+√3(3+2√35)/6]/√3=
√3[4/3+(3+2√35)/6]/√3=(8+3+2√35/6)/6=4/3+1/2+√35/3
A/B=4√3/3/(√3(3+2√35)/6)=
4√3/3•6/√3(3+2√35)= 4•2/(3+2√35)=8/(3+2√35).