ĐK \(x\ge2\)
\(\Leftrightarrow\left(\sqrt{x+1}-\sqrt{x-2}\right)\left(\sqrt{x+1}+\sqrt{x-2}\right)\left(1+\sqrt{\left(x+1\right)\left(x-2\right)}\right)=3\left(\sqrt{x+1}+\sqrt{x-2}\right)\)
\(\Leftrightarrow1+\sqrt{\left(x+1\right)\left(x-2\right)}=\sqrt{x+1}+\sqrt{x-2}\)
\(\Leftrightarrow\left(1+\sqrt{\left(x+1\right)\left(x-2\right)}\right)^2=\left(\sqrt{x+1}+\sqrt{x-2}\right)^2\)
\(\Leftrightarrow1+\left(x+1\right)\left(x-2\right)+2\sqrt{\left(x+1\right)\left(x-2\right)}\text{}\text{}=x+1+x-2+2\sqrt{\left(x+1\right)\left(x-2\right)}\)
\(\Leftrightarrow x^2-3x\text{}=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(l\right)\\x=3\left(nh\right)\end{matrix}\right.\)
vậy \(S=\left\{3\right\}\)
