1: \(-8x^3-36x^2+54x-35=0\)
=>\(8x^3+36x^2-54x+35=0\)
=>\(x\simeq-5,8\)
2: \(\dfrac{x^3}{27}-\dfrac{2}{3}x^2+4x-8=0\)
=>\(\left(\dfrac{x^3}{27}-8\right)-2x\left(\dfrac{1}{3}x-2\right)=0\)
=>\(\left(\dfrac{1}{3}x-2\right)\left(\dfrac{1}{9}x^2+\dfrac{2}{3}x+4\right)-2x\left(\dfrac{1}{3}x-2\right)=0\)
=>\(\left(\dfrac{1}{3}x-2\right)\left(\dfrac{1}{9}x^2+\dfrac{2}{3}x+4-2x\right)=0\)
=>\(\left(\dfrac{1}{3}x-2\right)\left(\dfrac{1}{9}x^2-\dfrac{4}{3}x+4\right)=0\)
=>\(\left[{}\begin{matrix}\dfrac{1}{3}x-2=0\\\dfrac{1}{9}x^2-\dfrac{4}{3}x+4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{3}x=2\\\dfrac{1}{9}x^2-2\cdot\dfrac{1}{3}x\cdot2+2^2=0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=6\\\left(\dfrac{1}{3}x-2\right)^2=0\end{matrix}\right.\Leftrightarrow x=6\)