\(x+\sqrt{x+\dfrac{1}{2}+\sqrt{x+\dfrac{1}{4}}}=2\)
\(\Leftrightarrow x+\sqrt{x+\dfrac{1}{4}+2\cdot\dfrac{1}{2}\cdot\sqrt{x+\dfrac{1}{4}}+\dfrac{1}{4}}=2\)
\(\Leftrightarrow x+\sqrt{\left(\sqrt{x+\dfrac{1}{4}}+\dfrac{1}{2}\right)^2}=2\)
\(\Leftrightarrow x+\sqrt{x+\dfrac{1}{4}}+\dfrac{1}{2}=2\)
\(\Leftrightarrow\sqrt{x+\dfrac{1}{4}}=\dfrac{3}{2}-x\left(đk:-\dfrac{1}{4}\le x\le\dfrac{3}{2}\right)\)
\(\Leftrightarrow x+\dfrac{1}{4}=\dfrac{9}{4}-3x+x^2\)
\(\Leftrightarrow x^2-4x+2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2+\sqrt{2}\left(loai\right)\\x=2-\sqrt{2}\end{matrix}\right.\)
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