a) \(x^4-24x+32=0\)
\(\Leftrightarrow x^4-2x^3+2x^3-4x^2+4x^2-8x-16x+32=0\)
\(\Leftrightarrow x^3\left(x-2\right)+2x^2\left(x-2\right)+4x\left(x-2\right)-16\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x^3+2x^2+4x-16\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x^3+2x^2+4x-16=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x\approx1,62\end{matrix}\right.\)
b) \(x^4-8x\sqrt{2}+12=0\)
\(\Leftrightarrow x^4-\sqrt{2}x^3+\sqrt{2}x^3-2x^2+2x^2-2\sqrt{2}x-6\sqrt{2}x+12=0\)
\(\Leftrightarrow x^3\left(x-\sqrt{2}\right)+\sqrt{2}x^2\left(x-\sqrt{2}\right)+2x\left(x-\sqrt{2}\right)-6\sqrt{2}\left(x-\sqrt{2}\right)=0\)
\(\Leftrightarrow\left(x-\sqrt{2}\right)\left(x^3+\sqrt{2}x^2+2x-6\sqrt{2}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{2}\\x\approx1,4142135...\end{matrix}\right.\)
