\(\left(x-1\right)\left(x-2\right)\left(x-3\right)\left(x-6\right)=15x^2\)
\(\Leftrightarrow\left(x^2-7x+6\right)\left(x^2-5x+6\right)-15x^2=0\) (*)
-Đặt \(t=x^2-5x+6\)
(*) \(\Leftrightarrow t\left(t-2x\right)-15x^2=0\)
\(\Leftrightarrow t^2-2xt-15x^2=0\)
\(\Leftrightarrow t^2-5xt+3xt-15x^2=0\)
\(\Leftrightarrow t\left(t-5x\right)+3x\left(t-5x\right)=0\)
\(\Leftrightarrow\left(t-5x\right)\left(t+3x\right)=0\)
\(\Leftrightarrow t-5x=0\) hay \(t+3x=0\)
\(\Leftrightarrow x^2-5x+6-5x=0\) hay \(x^2-5x+6+3x=0\)
\(\Leftrightarrow x^2-10x+6=0\) hay \(x^2-2x+6=0\)
\(\Leftrightarrow x^2-2.5x+25-19=0\) hay \(\left(x-1\right)^2+5=0\) (pt vô nghiệm)
\(\Leftrightarrow\left(x-5\right)^2-19=0\)
\(\Leftrightarrow\left(x-5-\sqrt{19}\right)\left(x-5+\sqrt{19}\right)=0\)
\(\Leftrightarrow x=5+\sqrt{19}\) hay \(x=5-\sqrt{19}\)
-Vậy \(S=\left\{5+\sqrt{19};5-\sqrt{19}\right\}\)
