Hello all, Need your help
Solve in $\displaystyle [-1,1]$ the equation : $\displaystyle \; (x+1)^2 = \sqrt{(1-x)^3} $
It's actually
$\displaystyle x(x^3 + 5x^2 + 3x + 7) = 0$.
Clearly $\displaystyle x = 0$ is a solution.
Try graphing the equation $\displaystyle x^3 + 5x^2 + 3x + 7$.
Clearly it has one root at about $\displaystyle x = -4.65$, but I don't believe there's a way to solve it exactly (I may be wrong).
You might want to use a Heuristic method like the Bisection Method or Newton's Method to increase the accuracy.
Edit: And as Mr F says, it doesn't lie in the domain anyway... this post is for future reference :P