\(x^2-6x+11=x^2-2\times3\times x+3^2+2=\left(x-3\right)^2+2\)
vì \(\left(x-3\right)^2\ge0\Rightarrow\left(x-3\right)^2+2\ge2\)
vậy MIN = 2 . dấu = xảy ra <=> x = 3
\(x^2-20x+101=x^2-2\cdot10\cdot x+10^2+1=\left(x-10\right)^2+1\)
vì\(\left(x-10\right)^2\ge0\Rightarrow\left(x-10\right)^2+1\ge1\)
vậy Min = 1 . dấu = xảy ra <=> x = 10
C) \(x^2-4xy+5y^2+10x-22y+28\)
\(\left(x^2-4xy+4y^2+10x-20y+25\right)+\left(y^2-2y+1\right)+2\)
\(\left(x-2y+5\right)^2+\left(y-1\right)^2+2\)>2
Vậy GTNN=2\(\Leftrightarrow X=-3;y=1\)