b) ĐKXĐ: \(x\ne2\)
\(\left|\dfrac{x+2}{x-2}\right|=2\)
\(\Leftrightarrow\dfrac{x+2}{x-2}=2\) hay \(\dfrac{x+2}{x-2}=-2\)
\(\Leftrightarrow\dfrac{x+2}{x-2}=\dfrac{2\left(x-2\right)}{x-2}\) hay \(\dfrac{x+2}{x-2}=\dfrac{-2\left(x-2\right)}{x-2}\)
\(\Rightarrow x+2=2x-4\) hay \(x+2=-2x+4\)
\(\Rightarrow x-2x=-4-2\) hay \(x+2x=4-2\)
\(\Leftrightarrow-x=-6\) hay \(3x=2\)
\(\Leftrightarrow x=6\left(nhận\right)\) hay \(x=\dfrac{2}{3}\left(nhận\right)\)
-Vậy \(S=\left\{6;\dfrac{2}{3}\right\}\)
c) \(\left|x^2-x-2\right|=\left|x^2+2x\right|\)
\(\Leftrightarrow\left(x^2-x-2\right)^2=\left(x^2+2x\right)^2\)
\(\Leftrightarrow\left(x^2-x-2\right)^2-\left(x^2+2x\right)^2=0\)
\(\Leftrightarrow\left(x^2-x-2+x^2+2x\right)\left(x^2-x-2-x^2-2x\right)=0\)
\(\Leftrightarrow\left(2x^2+x-2\right)\left(-3x-2\right)=0\)
\(\Leftrightarrow2x^2+x-2=0\) hay \(-3x-2=0\)
\(\Leftrightarrow x^2+\dfrac{1}{2}x-1=0\) hay \(x=\dfrac{-2}{3}\)
\(\Leftrightarrow x^2+2.\dfrac{1}{4}x+\dfrac{1}{16}-\dfrac{17}{16}=0\) hay \(x=\dfrac{-2}{3}\)
\(\Leftrightarrow\left(x+\dfrac{1}{4}\right)^2-\dfrac{17}{16}=0\) hay \(x=\dfrac{-2}{3}\)
\(\Leftrightarrow\left(x+\dfrac{1}{4}+\dfrac{\sqrt{17}}{4}\right)\left(x+\dfrac{1}{4}-\dfrac{\sqrt{17}}{4}\right)=0\) hay \(x=\dfrac{-2}{3}\)
\(\Leftrightarrow x=-\dfrac{1+\sqrt{17}}{4}\) hay \(x=-\dfrac{1-\sqrt{17}}{4}\) hay \(x=\dfrac{-2}{3}\)
-Vậy \(S=\left\{\dfrac{-1+\sqrt{17}}{4};\dfrac{-1-\sqrt{17}}{4};\dfrac{-2}{3}\right\}\)