\(N=\left(x-1\right)\left(x-3\right)+11\)
\(\Leftrightarrow N=x^2-3x-x+3+11\)
\(\Leftrightarrow N=x^2-4x+14\)
\(\Leftrightarrow N=\left(x^2-4x+4\right)+10\)
\(\Leftrightarrow N=\left(x-2\right)^2+10\)
Vậy GTNN của \(N=10\) khi \(x-2=0\Leftrightarrow x=2\)