Question

Aratati ca numerele a si b sunt naturale.

Answer 1

7.

inmultim fiecare termen cu conjugatul numitorului si observam diferenta de patrate

1/(√1+√2)=(1-√2)/(1-√2)(√1+√2)=(1-√2)/(1-2)= √2-1

1/(√2+√3)=√3-√2

...

1/(√8-√9)=√9-√8

astfel ca suma S=3-1=2

6.√168=2√2*√21

4√(21/2)=4*√2*√21/2=2√2√21

6√14/3)=6√(2*7/3)=6√2*21/9)=2√2*√21

√(4si 2/3)=√(14/3)=√2*√21/3 iar [√(4si 2/3)] la-1= 3/(√2*√21)

a=[2√2*√21]/[ 3/(√2*√21)]=[2√2*√21]*[√2*√21/3}=4*21/3=28