Question

efectuati: a)4supra √2-1+5supra√2+1-7supra3-√2 .
b)2supra2√7-5+11 supra3√2-√7-5supra√7-√2... c)1supra√2+1+1supra√3+√2+1supra√4+√3+1supra√5+√4...
d)(1supra√6+√5+1supra√7+√6+1supra√8+√7+1supra√9+√8)*1supra3-√5

Answer 1

a)4/(√2-1) +5/(√2+1)-7/(3-√2)=
=4(√2+1)/(2-1)+5(√2-1)/(2-1)-7(3+√2)/(9-2)=
=4√2+4+5√2-5-3-√2=
=8√2-4=
=4(2√2-1)

b)2/(2√7-5)+11/(3√2-√7)-5/(√7-√2)=
=2(2√7+5)/(28-25)+11(3√2+√7)/(18-7)-5(√7+√2)/(7-2)=
=2(2√7+5)/3+11(3√2+√7)/11-5(√7+√2)/5=
=2(2√7+5)/3+3√2+√7-√7-√2=
=2(2√7+5)/3+2√2=
=(4√7+10+6√2)/3

c)1/(√2+1)+1/(√3+√2)+1/(√4+√3)+1/(√5+√4)=
=1(√2-1)/(2-1)+1(√3-√2)/(3-2)+1(√4-√3)/(4-3)+1(√5-√4)/(5-4)==√2-1+√3-√2+√4-√3+√5-√4=
=-1+√5=
=√5-1

d)[1/(√6+√5)+1/(√7+√6)+1/(√8+√7)+1/(√9+√8)]*1/(3-√5)=
=[1(√6-√5)/(6-5)+1(√7-√6)/(7-6)+1(√8-√7)/(8-7)+1(3-√8)/(9-8)]* 
*1(3+√5)/(9-5)= (√6-√5+√7-√6+√8-√7+3-√8)*(3+√5)/4= 
=(3-√5)*(3+√5)/4=(9-5) /4=1