Prepping for the GMAT, I came across the following question:
What is the product of all solutions of:
$$x^2 - 4x + 6 = 3 - |x - 1|?$$
First, I set up two equations, ie:
$$x^2 - 4x + 6 = 3 - (x - 1),$$ and $$x^2 - 4x + 6 = 3 - (-1) \times (x - 1).$$
These factor down to $3$ solutions: $1$, $2$ and $4$. And $8$ is correct solution in the back of the prep book.
However, when plugging $4$ back into the original equation, it reduces to $6 = 3$, so $4$ does not seem to be a solution. Also, when graphing both, they only intersect at $1$ and $2$.
What part of my process (and seemingly the practice books process) is wrong?