Question

Buna, am o problema la mate care suna cam asa:
"Sa se demonstreze ca numarul
N=(2-√3)²+(3+√3)²–2√3
Este natural"
Multumesc anticipat! :)

Answer 1

$N=(2- \sqrt{3} )^2+(3+ \sqrt{3} )^2-2 \sqrt{3} \\ N=2^2-2*2* \sqrt{3} + \sqrt{3} ^2+3^2+2*3* \sqrt{3} + \sqrt{3} ^2-2 \sqrt{3} \\ N=4-4 \sqrt{3} +3+9+6 \sqrt{3} +3-2 \sqrt{3} \\ N=4+3+9+3$
$N=19$ ∈ $N$