Question

Cat este a astfel incat x*x+y*y+z*z-4x-2y+2z+a>0

Answer 1

$x^{2} + y^{2} + z^{2} -4x-2y+2z= \\ = (x^{2} -4x+4) +(y^{2}-2y+1) +(z^{2}+2z+1)-6= \\ =(x-2 )^{2} +(y-1)^{2}+(z+1)^{2}-6$

Cum $(x-2)^{2}+(y-1)^{2}+(z+1)^{2} -6 \geq 0-6=-6.$, deducem ca a>6.