The least possible value How to find the least possible value for :$$(x-1)^2+(x-2)^2+(x-3)^2+(x-4)^2+(x-5)^2$$
For every real $x$

$(x-1)^2+(x-2)^2+(x-3)^2+(x-4)^2+(x-5)^2$
$=(y+2)^2+(y+1)^2+y^2+(y-1)^2+(y-2)^2$.Let $(y=(x-3))$
$=5y^2+2(1^2+2^2)\ge2(1^2+2^2)$
Equality occurs at $y=0\Rightarrow x=3$
