Question

e si f sa fie folosita rationalizarea

Answer 1

[2/(√7+√5) +2/(√5+√3)] : (1/√3-1/√7)=
=[2(√7-√5)/(7-5) +2(√5-√3)/(5-3)] : (√3/3-√7/7)=
=(√7-√5 +√5-√3) : (7√3-3√7/21)=
=(√7-√3) ×21/ (7√3-3√7)=
=21 ×(√7-√3)(7√3+3√7)/(7√3-3√7)(7√3+3√7)=
=21 ×(7√21-21+21-3√7)/84=
=4√21/4=√21


[2/(3√3+5)+1/(5+2√6)] · √3/(3-2√2)=
=[2(3√3-5)/(3√3+5)(3√3-5)+(5-2√6)/(5+2√6)(5-2√6)]·√3(3+2√2)/(3-2√2)(3+2√2)=
=[2(3√3-5)/(27-25)+(5-2√6)/(25-24)]·√3(3+2√2)/(9-8)=
=[(3√3-5)+(5-2√6)]·√3(3+2√2)=
=(3√3-5+5-2√6)·√3(3+2√2)=
=√3(3-2√2)·√3(3+2√2)=
=3(9-8)=3