\(A=\frac{2}{6x-5-9x^2}\)
\(\Leftrightarrow A=\frac{-2}{9x^2-6x+5}\)
\(\Leftrightarrow A=\frac{-2}{\left(3x-1\right)^2+4}\)
Vì \(\left(3x-1\right)^2\ge0\forall x\Rightarrow\left(3x-1\right)^2+4\ge4\)
\(\Rightarrow\frac{1}{\left(3x-1\right)^2+4}\le\frac{1}{4}\)
\(\Rightarrow\frac{-2}{\left(3x-1\right)^2+4}\ge\frac{-2}{4}\)
\(\Rightarrow A\ge\frac{-1}{2}\)
\(MinA=\frac{-1}{2}\Leftrightarrow3x-1=0\Leftrightarrow x=\frac{1}{3}\)
Ta có: A = \(\frac{2}{6x-5-9x^2}=\frac{2}{-\left(9x^2-6x+1\right)-4}=\frac{2}{-\left(3x-1\right)^2-4}\ge-\frac{1}{2}\)
Dấu "=" xảy ra <=> \(3x-1=0\) <=> \(x=\frac{1}{3}\)
Vậy MinA = -1/2 <=> x= 1/3
