linear algebra - What is the number of real solutions of the equation $ | x - 3 | ^ { 3x^2 -10x + 3 } = 1 $?

I did solve, I got four solutions, but the book says there are only 3.

I considered the cases $| x - 3 | = 1$ or $3x^2 -10x + 3 = 0$.

I got for $x\leq 0$: $~2 , 3 , \frac13$

I got for $x > 0$: $~4$

Am I wrong? Is $0^0 = 1$ or NOT?

Considering the fact that : $ 2^2 = 2 \cdot2\cdot 1 $

$2^1 = 2\cdot 1$

$2^0 = 1$

$0^0$ should be $1$ right?