Question

Aratati ca numarul n=|2√2 -2|+(√2+1)² este numar natural

Answer 1

[tex]|2 \sqrt{2} -2|=\ \textgreater \ (2 \sqrt{2} ) ^{2} ...2 ^{2} =\ \textgreater \ \\ 8\ \textgreater \ 4=\ \textgreater \ 2 \sqrt{2} -2\ \textgreater \ 0=\ \textgreater \ |2 \sqrt{2} -2|\ \textgreater \ 0=\ \textgreater \ |2 \sqrt{2} -2|=-2 \sqrt{2}+2 \\ ( \sqrt{2} +1) ^{2} =2+2 \sqrt{2} +1=3+2 \sqrt{2} \\ n=|2 \sqrt{2} -2|+( \sqrt{2} +1) ^{2}=-2 \sqrt{2}+2+3+2 \sqrt{2}=5[/tex]