Question

Sa se arate ca (1+√7)² + (1-√7)² este nr. natural! Rezolvarea!

Answer 1

$\bold{(1+ \sqrt{7} )^2+(1- \sqrt{7} )^2=} \\ \bold{=1^2+2 \cdot 1 \cdot \sqrt{7} + \sqrt{7} ^2+1^2-2 \cdot 1 \cdot \sqrt{7} + \sqrt{7} ^2=} \\ \bold{1+2 \sqrt{7} +7+1-2 \sqrt{7} +7=1+7+1+7=16 \in N}$