* GTNN:
Ta có: \(C=\dfrac{6x+11}{x^2-2x+3}=\dfrac{12x+22}{x^2-2x+3}=\dfrac{-\left(x^2-2x+3\right)+\left(x^2+10x+25\right)}{2\left(x^2-2x+3\right)}\)
\(=-\dfrac{1}{2}+\dfrac{\left(x+5\right)^2}{2\left(x^2-2x+3\right)}\ge-\dfrac{1}{2}\)
Dấu "=" xảy ra \(\Leftrightarrow x+5=0\Leftrightarrow x=-5\)
* GTLN
Ta có: \(C=\dfrac{6x+11}{x^2-2x+3}=\dfrac{9x^2-18x+27-\left(9x^2-24x+16\right)}{x^2-2x+3}\)
\(=9-\dfrac{\left(3x-4\right)^2}{x^2-2x+3}\le9\)
Dấu "=" xảy ra \(\Leftrightarrow3x-4=0\Leftrightarrow x=\dfrac{4}{3}\)
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