Is this enough for a proof?:
$$x^3+x^2 = 1$$
I would factor and get: $x^2(x+1) = 1$
I would show that $x = \sqrt1$, which is irrational but then do I have to show more? $x+1=1$ which gives me $x=0$ and since $x$ cannot equal to $0$ as this would make the statement false (everything is $0$). Is it enough to simply state this falsity or is there another way to express it?