c: \(x^2-8x+16=5\left(4-x\right)^3\)
=>\(\left(x-4\right)^2-5\left(4-x\right)^3=0\)
=>\(\left(x-4\right)^2+5\left(x-4\right)^3=0\)
=>\(\left(x-4\right)^2\cdot\left(x-4+5\right)=0\)
=>\(\left(x-4\right)^2\cdot\left(x+1\right)=0\)
=>\(\left[{}\begin{matrix}x-4=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-1\end{matrix}\right.\)
d: \(\left(2-x\right)^3=6x\left(x-2\right)\)
=>\(8-12x+6x^2-x^3=6x^2-12x\)
=>\(8-x^3=0\)
=>\(x^3=8=2^3\)
=>x=2
e: \(\left(x+1\right)^3-\left(x-1\right)^3-6\left(x-1\right)^2=-10\)
=>\(x^3+3x^2+3x+1-\left(x^3-3x^2+3x-1\right)-6\left(x^2-2x+1\right)=-10\)
=>\(x^3+3x^2+3x+1-x^3+3x^2-3x+1-6\left(x^2-2x+1\right)=-10\)
=>\(6x^2+2-6x^2+12x-6=-10\)
=>12x-4=-10
=>12x=-6
=>\(x=-\dfrac{1}{2}\)
f: \(\left(3-x\right)^3-\left(x+3\right)^3=36x^2-54x\)
=>\(27-27x+9x^2-x^3-x^3-9x^2-27x-27=36x^2-54x\)
=>\(-2x^3-54x+36x^2+54x=0\)
=>\(-2x^3+36x^2=0\)
=>\(x^3-18x^2=0\)
=>\(x^2\left(x-18\right)=0\)
=>\(\left[{}\begin{matrix}x^2=0\\x-18=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=18\end{matrix}\right.\)
