\(A=x^2-2x+2\\ A=x^2-2x+1+1\\ A=\left(x-1\right)^2+1\)
Có \(\left(x-1\right)^2\ge0\forall x\)
\(\Rightarrow\left(x-1\right)^2+1\ge1\forall x\\ \Rightarrow A\ge1\forall x\\ \Rightarrow\min\limits_A=1\)
Dấu "=" xảy ra \(\Leftrightarrow\left(x-1\right)^2=0\\ \Leftrightarrow x-1=0\\ \Leftrightarrow x=1\)
Vậy \(\min\limits_A=1\) khi x = 1
\(A=x^2-2x+2\\ A=x^2-2x+1+1\\ A=\left(x-1\right)^2+1\)
Ta có:
\(\left(x-1\right)^2\ge0\\ \Rightarrow\left(x-1\right)^2+1\ge1\)
hay \(A\ge1\)
Dấu \("="\) xảy ra khi \(x=1\)
Vậy GTNN của A là 1 khi \(x=1\)
