Solving the equation : $x^3 - 1001x + 1000 = 0$

Question

$$x^3 - 1001x + 1000$$ Let : $x=(v+u)$

$v^3+u^3+1000=(v+u)(1000-3uv)$

$v^3+u^3+1000=3(v+u)(1000/3-uv)$

$(1000/3-uv)=0$

$uv=1000/3$

Answer : $x=1$

How can $1$ divide into two values $(v \quad \text{and} \quad u)$ and their product is $1000/3$

Answer 1

use that $x=1$ is one solution and divide $$x^3-1001x+1000$$ by $$x-1$$ for your Control we get $$(x-1) \left(x^2+x-1000\right)$$