If (x - 3)2 + (y - 5)2 + (z - 4)2 = 0, then the value of x^29 + y^225 + z^216 is?

Answer: Option C

$$\begin{array}{rl}& {\left(x-3\right)}^2\text{ + }{\left(y-5\right)}^2\text{ + }{\left(z-4\right)}^2=0\\ & \therefore {\left(x-3\right)}^2=0x=3\\ & {\left(y-5\right)}^2=0y=5\\ & {\left(z-4\right)}^2=0z=4\\ & \therefore \frac{x^2}{9}\text{ + }\frac{y^2}{25}\text{ + }\frac{z^2}{16}\\ & \Rightarrow \frac{9}{9}+\frac{25}{25}+\frac{16}{16}\\ & \Rightarrow 3\end{array}$$