ĐKXĐ: \(-\sqrt{\dfrac{5}{2}}\le x\le\sqrt{\dfrac{5}{2}}\)
\(2\left(2x-1\right)\sqrt{10-4x^2}=10-4x\)
\(\Leftrightarrow2\left(2x-1\right)\sqrt{10-4x^2}=10-4x^2+4x^2-4x+1-1\)
\(\Leftrightarrow\left(2x-1\right)^2-2\left(2x-1\right)\sqrt{10-4x^2}+10-4x^2-1=0\)
\(\Leftrightarrow\left(2x-1-\sqrt{10-4x^2}\right)^2-1=0\)
\(\Leftrightarrow\left(2x-2-\sqrt{10-4x^2}\right)\left(2x-\sqrt{10-4x^2}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{10-4x^2}=2x-2\left(x\ge1\right)\\\sqrt{10-4x^2}=2x\left(x\ge0\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}10-4x^2=4x^2-8x+4\left(x\ge1\right)\\10-4x^2=4x^2\left(x\ge0\right)\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=\dfrac{\sqrt{5}}{2}\end{matrix}\right.\)
