What is the sum of all real numbers $x$ such that $(x^2-5x+5)^{(x^2-7x+12)}=1$?
So I know that $x^0=1$ and $1^x=1$. So, I can solve for them and find $x$, and add them up.
Solving $x^2-7x+12=0$ for $x^0=1$ gives $x=3, 4$.
Solving $x^2-5x+5=1$ for $1^x=1$ gives $x=1, 4$.
Adding them up gives $1+3+4=8$.
This is wrong. What did I do wrong? Did I miss a case? If so, what case have I missed?
Thanks!
Max0815