I have been solving some questions on algebra until I came across this question:
If $x, y$, and $z$ are real number such that $$(x - 3)^2 + (y - 4)^2 + (z - 5)^2 = 0$$
find the value of $$x + y + z$$.
So first, I expanded the equation. Then, I factorised it again leaving x, y and z out which left me with this equation:
$$x(x - 6) + y(y - 8) + z(z - 10) = -50$$
I thought this was the correct way to approach this question. However, I cannot take any further steps. Can someone please give me hints on how to approach this question?
Thanks in advance.