-Khi \(x\ge3\) thì:
\(PT\Leftrightarrow x-1+x-2+x-3=-x^2+4x-2\)
\(\Leftrightarrow3x-6=-x^2+4x-2\)
\(\Leftrightarrow x^2-x-4=0\)
\(\Leftrightarrow\left(x-\dfrac{1}{2}\right)^2-\dfrac{17}{4}=0\)
\(\Leftrightarrow\left(x-\dfrac{1}{2}-\dfrac{\sqrt{17}}{2}\right)\left(x-\dfrac{1}{2}+\dfrac{\sqrt{17}}{2}\right)=0\)
\(\Leftrightarrow x=\dfrac{1\pm\sqrt{17}}{2}\left(nhận\right)\)
-Khi \(2\le x< 3\) thì:
\(PT\Leftrightarrow x-1+x-2+3-x=-x^2+4x-2\)
\(\Leftrightarrow x=-x^2+4x-2\)
\(\Leftrightarrow x^2-3x+2=0\)
\(\Leftrightarrow x^2-2x-x+2=0\)
\(\Leftrightarrow x\left(x-2\right)-\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\left(nhận\right)\\x=1\left(loại\right)\end{matrix}\right.\)
-Khi \(1\le x< 2\) thì:
\(PT\Leftrightarrow x-1+2-x+3-x=-x^2+4x-2\)
\(\Leftrightarrow-x+4=-x^2+4x-2\)
\(\Leftrightarrow x^2-5x+6=0\)
\(\Leftrightarrow x^2-2x-3x+6=0\)
\(\Leftrightarrow x\left(x-2\right)-3\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\left(loại\right)\\x=3\left(loại\right)\end{matrix}\right.\)
-Khi \(x< 1\) thì:
\(PT\Leftrightarrow1-x+2-x+3-x=-x^2+4x-2\)
\(\Leftrightarrow-3x+6=-x^2+4x-2\)
\(\Leftrightarrow x^2-7x+8=0\)
\(\Leftrightarrow\left(x-\dfrac{7}{2}\right)^2-\dfrac{17}{4}=0\)
\(\Leftrightarrow\left(x-\dfrac{7}{2}-\dfrac{\sqrt{17}}{2}\right)\left(x-\dfrac{7}{2}+\dfrac{\sqrt{17}}{2}\right)=0\)
\(\Leftrightarrow x=\dfrac{7\pm\sqrt{17}}{2}\left(loại\right)\)
-Tổng kết lại vậy \(S=\left\{2;\dfrac{1\pm\sqrt{17}}{2}\right\}\)
