\(6x-3\sqrt{3x-6}=12\)
ĐK:\(x\ge 2\)
\(pt\Leftrightarrow-3\sqrt{3x-6}-\left(-6x+12\right)=0\)
\(\Leftrightarrow\dfrac{9\left(3x-6\right)-\left(-6x+12\right)^2}{-3\sqrt{3x-6}+\left(-6x+12\right)}=0\)
\(\Leftrightarrow\dfrac{27x-54-36x^2+144x-144}{-3\sqrt{3x-6}-6x+12}=0\)
\(\Leftrightarrow\dfrac{-9\left(x-2\right)\left(4x-11\right)}{-3\sqrt{3x-6}-6x+12}=0\)
Dễ thấy: \(\dfrac{-9}{-3\sqrt{3x-6}-6x+12}>0\forall x\ge2\)
\(\Rightarrow\left(x-2\right)\left(4x-11\right)=0\)\(\Rightarrow\left[{}\begin{matrix}x=2\\x=\dfrac{11}{4}\end{matrix}\right.\)
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