Question

Pe mutimea numerelor reale se defineste legea de compozitie: x*y=2018(xy-x-y)+2019
Determinati numerele intregi n, cu proprietatea n*n ≤ 2019

Answer 1

$n*n\leq2019\\2018(n^2-n-n)+2019\leq2019\\2018(n^2-2n)\leq0\\n(n-2)\leq0\\n(n-2)=0\Rightarrow n=0\text{ sau }n-2=0\Rightarrow n=0\text{ sau }n=2\\\text{Din tabel }\Rightarrow n\in\left[0,2\right]\\\text{Dar }n\in\mathbb{Z}\Rightarrow n\in [0,2]\cap\mathbb{Z}\Rightarrow n\in\{0, 1, 2\}$