Question

Determinati numerele reale x si y care verifica egalitatea:x la puterea a 2a +y la puterea a 2a -4x-6y+13=0.

Answer 1

$x^2+y^2-4x-6y+13=0 \\\\ \hbox{Incercam sa formam binoame scriind nr. 13 ca suma de 2 numere } \\\\\\ x^2-4x+4+ y^2-6y+9=0 \\\\ (x-2)^2+(y-3)^2=0 \\\\\\ 1) (x-2)^2=0 \\\\ x-2=0 \longrightarrow \boxed{x=2} \\\\\\ 2)(y-3)^2=0 \\\\ y-3=0 \longrightarrow \boxed{y=3}$