If a2 + b2 + c2 + 84 = 4(a - 2b + 4c), then ab - bc + ca is equal to:

Answer: Option D

$$\begin{array}{rl}& a^2+b^2+c^2+84=4\left(a-2b+4c\right)\\ & a=2\\ & b=-4\\ & c=8\\ & =\sqrt{ab-bc+ca}\\ & =\sqrt{2\times \left(-4\right)-\left(-4\right)\times 8+8\times 2}\\ & =\sqrt{32+8}\\ & =\sqrt{40}\\ & =2\sqrt{10}\end{array}$$