Question

cum se rezolva asta: Determinati x+y+z stiind ca X² +y²+ z²+=4x +6y-2z+14=0

Answer 1

x^2+y^2+z^2+4x+6y-2z+14=0 <=> (x^2+4x+4)+(y+6y+9)+(z-2z+1)=0 <=> (x+2)^2+(y+3)^2+(z-1)^2=0 <=> x+2=0 si y+3=0 si z-1=0 <=> x=-2 si y=-3 si z=1.

Deci x+y+z=-2-3+1=-4.

PS: am presupus ca x,y,z apartin R (deoarece n-ai specificat).