Question

Answer 1

\(\left(x-1\right)^3+3\left(x+1\right)^2=\left(x^2-2x+4\right)\left(x+2\right)\)

\(\Rightarrow x^3-3x^2+3x-1+3x^2+6x+3=x^3+8\)

\(\Rightarrow9x=6\Rightarrow x=\dfrac{2}{3}\)

Answer 2

\(\Leftrightarrow x^3-3x^2+3x-1+3x^2+6x+3=x^3-8\)

\(\Leftrightarrow9x=-10\)

hay \(x=-\dfrac{10}{9}\)

Answer 3

(x-1)³+3(x+1)²=(x²-2x+4)(x+2)
=>(x-1)³+3(x+1)²=x³+8
=>x³-3x²+3x-1+3(x²+2x+1)-x³-8=0
=>x³-3x²+3x-1+3x²+6x+3-x³-8=0
9x-9=0
9x=9
x=1