\(\Leftrightarrow x^2-6x+8=6\sqrt{2x+1}-18\left(Đk:x\ge-\dfrac{1}{2}\right)\)
\(\Leftrightarrow\left(x-2\right)\left(x-4\right)=\dfrac{12\left(x-4\right)}{\sqrt{2x+1}+3}\left(\sqrt{2x+1}+3>0\right)\)
+) \(x=4\left(TM\right)\)
+) \(x\ne4\Rightarrow x-2=\dfrac{12}{\sqrt{2x+1}+3}\)
\(\Leftrightarrow x-4=\dfrac{12-2\left(\sqrt{2x+1}+3\right)}{\sqrt{2x+1}+3}\)
\(\Leftrightarrow x-4+\dfrac{2\left(x-4\right)}{\left(\sqrt{2x+1}+3\right)^2}=0\)
\(\Leftrightarrow1+\dfrac{2}{\left(\sqrt{2x+1}+3\right)^2}=0\left(x\ne4\right)\)
Vì \(\dfrac{2}{\left(\sqrt{2x+1}+3\right)^2}>0\forall x\) => VT>0
=> phương trình vô nghiệm
Vậy \(S=\left\{4\right\}\)
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