1. Với \(x^2-2\ge0\Rightarrow\orbr{\begin{cases}x\ge\sqrt{2}\\x\le-\sqrt{2}\end{cases}}\)
Pt\(\Leftrightarrow x^4-4x^2+5x^2-10+8=0\Rightarrow x^4+x^2-2=0\)
\(\Leftrightarrow\left(x^2-2\right)\left(x^2+1\right)=0\Rightarrow x^2=2\Rightarrow\orbr{\begin{cases}x=\sqrt{2}\\x=-\sqrt{2}\end{cases}\left(tm\right)}\)
Với \(x^2-2< 0\Rightarrow-\sqrt{2}< x< \sqrt{2}\)
Pt \(\Leftrightarrow x^4-4x^2+10-5x^2+8=0\Leftrightarrow x^4-9x^2+18=0\)
\(\Leftrightarrow\orbr{\begin{cases}x^2-6=0\\x^2-3=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x^2=6\\x^2=3\end{cases}\left(l\right)}\)vì \(x\notin\left(-\sqrt{2};\sqrt{2}\right)\)
2. \(2x^4-20x+18=0\Rightarrow x^4-10x+9=0\)
\(\Rightarrow\left(x^4-x^3\right)+\left(x^3-x^2\right)+\left(x^2-x\right)-\left(9x-9\right)=0\)
\(\Rightarrow\left(x-1\right)\left(x^3+x^2+x-9\right)=0\Rightarrow\orbr{\begin{cases}x=1\\x^3+x^2+x-9=0\end{cases}}\)
\(\Rightarrow x=1\)
