\(\left|\dfrac{5}{6}-3x\right|>=0\forall x\)
=>\(\left|\dfrac{5}{6}-3x\right|+5>=5\forall x\)
=>\(Q=\dfrac{8}{\left|\dfrac{5}{6}-3x\right|+5}< =\dfrac{8}{5}\forall x\)
Dấu '=' xảy ra khi \(\dfrac{5}{6}-3x=0\)
=>\(3x=\dfrac{5}{6}\)
=>\(x=\dfrac{5}{18}\)
\(Q=\dfrac{8}{5+\left|\dfrac{5}{6}-3x\right|}\)
Ta thấy: \(\left|\dfrac{5}{6}-3x\right|\ge0\forall x\)
\(\Rightarrow5+\left|\dfrac{5}{6}-3x\right|\ge5\forall x\)
\(\Rightarrow\dfrac{1}{5+\left|\dfrac{5}{6}-3x\right|}\le\dfrac{1}{5}\forall x\)
\(\Rightarrow Q=\dfrac{8}{5+\left|\dfrac{5}{6}-3x\right|}\le\dfrac{8}{5}\forall x\)
Dấu \("="\) xảy ra khi: \(\dfrac{5}{6}-3x=0\Leftrightarrow3x=\dfrac{5}{6}\)
\(\Leftrightarrow x=\dfrac{5}{18}\)
Vậy \(Max_Q=\dfrac{8}{5}\) khi \(x=\dfrac{5}{18}\).
Đề như này phải không bạn?
