If x2 - 12x + 33 = 0, then what is the value of (x - 4)2 + 1 ( x - 4 )^2?

Answer: Option B

$$\begin{array}{rl}& x^2-12x+33=0\\ & x^2-12x+36-3=0\\ & {\left(x-6\right)}^2-3=0\\ & x=\sqrt{3}+6\\ & {\left(x-4\right)}^2+\frac{1}{{\left(x-4\right)}^2}\\ & \therefore {\left(\sqrt{3}+2\right)}^2+\frac{1}{{\left(\sqrt{3}+2\right)}^2}\\ & ={\left(\sqrt{3}+2\right)}^2+{\left(\sqrt{3}-2\right)}^2\\ & =2\left({\sqrt{3}}^2+2^2\right)\\ & =2\times 7\\ & =14\end{array}$$