Giải:
a) \(A\left(x\right)=4x^2-4x+3\)
\(\Leftrightarrow A\left(x\right)=4x^2-4x+1+2\)
\(\Leftrightarrow A\left(x\right)=\left(4x^2-4x+1\right)+2\)
\(\Leftrightarrow A\left(x\right)=\left(2x-1\right)^2+2\ge2;\forall x\)
\(\Leftrightarrow A\left(x\right)_{Min}=2\)
\("="\Leftrightarrow2x-1=0\Leftrightarrow x=\dfrac{1}{2}\)
Vậy ...
b) \(B\left(x\right)=6x-9x^2\)
\(B\left(x\right)=-9x^2+6x-1+1\)
\(B\left(x\right)=-\left(9x^2+6x+1\right)+1\)
\(B\left(x\right)=-\left(3x+1\right)^2+1\)
\(B\left(x\right)=-\left(3x+1\right)^2+1\le1;\forall x\)
\(\Rightarrow B\left(x\right)_{Max}=1\)
\("="\Leftrightarrow3x+1=0\Leftrightarrow x=-\dfrac{1}{3}\)
Vậy ...
