Question

O produto das raízes da equação (x + 2)² = x² é:

Answer 1

$\mathrm{\mathbf{1)}\ x^2=(x+2)^2\ \to\ x^2=x^2+4x+4}\\ \mathrm{0=4x+4\ \to\ 4x=-4\ \to\ \boxed{\mathbf{x=-1}}}\\\\ \mathrm{\mathbf{2)}\ x=\pm\sqrt{(x+2)^2}\ \to\ x=\pm(x+2)}\\ \mathrm{\mathbf{2.1)}\ x=x+2\ \to\ 0=2\ \to\ Abs!}\\ \mathrm{\mathbf{2.2)}\ x=-x-2\ \to\ 2x=-2\ \to\ \boxed{\mathbf{x=-1}}}\\\\ \boxed{\mathbf{S=\{x\in\mathbb{R}\ |\ x=-1\}}}$