a) \(A=x^2-20x+101=x^2-2.10x+100+1\)
\(=\left(x-10\right)^2+1\ge1\)
Vậy \(A_{min}=1\Leftrightarrow x=10\)
b) \(B=x^2-x+1=x^2-2.\frac{1}{2}x+\frac{1}{4}+\frac{3}{4}\)
\(=\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\ge\frac{3}{4}\)
Vậy \(B_{min}=\frac{3}{4}\Leftrightarrow x=\frac{1}{2}\)
c) \(C=2x^2+2x+1=2\left(x^2+x+\frac{1}{2}\right)\)
\(=2\left(x^2+2.\frac{1}{2}x+\frac{1}{4}+\frac{1}{4}\right)\)
\(=2\left[\left(x+\frac{1}{4}\right)^2+\frac{1}{4}\right]\ge\frac{1}{2}\)
Vậy \(C_{min}=\frac{1}{2}\Leftrightarrow x=\frac{-1}{4}\)
