Ta có: \(\left(x^2-6x\right)^2-2\left(x-3\right)^2+2=0\)
=>\(\left(x^2-6x+9-9\right)^2-2\left(x-3\right)^2+2=0\)
=>\(\left\lbrack\left(x-3\right)^2-9\right\rbrack^2-2\left(x-3\right)^2+2=0\)
=>\(\left(x-3\right)^4-18\left(x-3\right)^2+81-2\left(x-3\right)^2+2=0\)
=>\(\left(x-3\right)^4-20\left(x-3\right)^2+83=0\)
=>\(\left(x-3\right)^4-20\left(x-3\right)^2+100-17=0\)
=>\(\left\lbrack\left(x-3\right)^2-10\right\rbrack^2=17\)
=>\(\left[\begin{array}{l}\left(x-3\right)^2-10=\sqrt{17}\\ \left(x-3\right)^2-10=-\sqrt{17}\end{array}\right.\Rightarrow\left[\begin{array}{l}\left(x-3\right)^2=10+\sqrt{17}\\ \left(x-3\right)^2=10-\sqrt{17}\end{array}\right.\)
TH1: \(\left(x-3\right)^2=10+\sqrt{17}\)
=>\(\left[\begin{array}{l}x-3=\sqrt{10+\sqrt{17}}\\ x-3=-\sqrt{10+\sqrt{17}}\end{array}\right.\Rightarrow\left[\begin{array}{l}x=3+\sqrt{10+\sqrt{17}}\\ x=3-\sqrt{10+\sqrt{17}}\end{array}\right.\)
TH2: \(\left(x-3\right)^2=10-\sqrt{17}\)
=>\(\left[\begin{array}{l}x-3=\sqrt{10-\sqrt{17}}\\ x-3=-\sqrt{10-\sqrt{17}}\end{array}\right.\Rightarrow\left[\begin{array}{l}x=3+\sqrt{10-\sqrt{17}}\\ x=3-\sqrt{10-\sqrt{17}}\end{array}\right.\)
