Question

Stabiliti in ce intervale se afla numerele reale x, y, z care verifica relatia: x^2+4y^2+z^2+10=2(2x-2y-3z).

Answer 1

x^2+4y^2+z^2+10-4x+4y+6z=0
(x^2 - 4x+4)+(4y^2+4y+1)+(z^2+6z+9) - 4=0
(x-2)^2+(2y+1)^2+(z+3)^2 - 4=0
(x-2)^2≤4, |x-2|≤2, -2≤x-2≤2, 0≤x≤4
(2y+1)^2≤4, |2y+1|≤2, -2≤2y+1≤2, -3≤2y≤1, -3/2≤y≤1/2
(z+3)^2≤4, |z+3|≤2, -2≤z+3≤2, -5≤z≤-1