Question

Answer 1

a: \(x^3-9x=0\)

=>\(x\left(x^2-9\right)=0\)

=>x(x-3)(x+3)=0

=>\(\left[\begin{array}{l}x=0\\ x-3=0\\ x+3=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=3\\ x=-3\end{array}\right.\)

b: \(-64+48x-12x^2+x^3=0\)

=>\(x^3-3\cdot x^2\cdot4+3\cdot x\cdot4^2-4^3=0\)

=>\(\left(x-4\right)^3=0\)

=>x-4=0

=>x=4

c: \(x\left(2x-1\right)\left(x+5\right)-\left(2x^2+1\right)\left(x+4,5\right)=0\)

=>\(\left(2x^2-x\right)\left(x+5\right)-\left(2x^2+1\right)\left(x+4,5\right)=0\)

=>\(2x^3+10x^2-x^2-5x-2x^3-9x^2-x-4,5=0\)

=>-6x-4,5=0

=>-6x=4,5

=>x=-0,75