ĐKXĐ: \(x\ge\dfrac{-3}{2}\)
\(36x^2-2.6x\sqrt{8x+12}+8x+12-4x^2+4x-1=0\)
\(\Leftrightarrow\left(6x-\sqrt{8x+12}\right)^2-\left(2x-1\right)^2=0\)
\(\Leftrightarrow\left(4x-\sqrt{8x+12}+1\right)\left(8x-\sqrt{8x+12}-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}4x-\sqrt{8x+12}+1=0\left(1\right)\\8x-\sqrt{8x+12}-1=0\left(2\right)\end{matrix}\right.\)
TH1: \(4x-\sqrt{8x+12}+1=0\Leftrightarrow4x+1=\sqrt{8x+12}\)
\(\Leftrightarrow\left\{{}\begin{matrix}4x+1\ge0\\\left(4x+1\right)^2=8x+12\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ge\dfrac{-1}{4}\\16x^2=11\end{matrix}\right.\) \(\Rightarrow x=\dfrac{\sqrt{11}}{4}\)
TH2: \(8x-\sqrt{8x+12}-1=0\Leftrightarrow8x-1=\sqrt{8x+12}\)
\(\Leftrightarrow\left\{{}\begin{matrix}8x-1\ge0\\\left(8x-1\right)^2=8x+12\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ge\dfrac{1}{8}\\64x^2-24x-11=0\end{matrix}\right.\) \(\Rightarrow x=\dfrac{3+\sqrt{53}}{16}\)
