Question

Se considera numerele a=√mare din 2-√2 si b=√mare din 2+√2. Aratati b supra a -√2 apartine Q

Answer 1

a=rad(2-rad(2))=rad((2-rad(2))(2+rad(2))/(2+rad(2)))=rad(2/(2+rad(2)))=rad(2)/rad(2+rad(2))=rad(2)/b.

Deci b/a-rad(2)=b/(rad(2)/b)-rad(2)=b^2/rad(2)-rad(2)=(2+rad(2))/rad(2)-rad(2)=rad(2)/rad(2)=1 apartine Q.