If a3 + b3 = 218 and a + b = 2, then the value of 1 - ab is:

Answer: Option D

$$\begin{array}{rl}& a^3+b^3=218\&a+b=2\\ & {\left(a+b\right)}^3={\left(2\right)}^3\\ & a^3+b^3+3\left(a+b\right)\left(ab\right)=8\\ & 218+3\left(2\right)\left(ab\right)=8\\ & ab=\frac{8-218}{6}\\ & ab=\frac{-210}{6}=-35\\ & \sqrt{1-ab}=\sqrt{1-\left(-35\right)}\\ & \sqrt{1-ab}=\sqrt{1+\left(35\right)}\\ & \sqrt{1-ab}=6\end{array}$$