If $ 1 + 4x^2 + 16x^4 = 512 $, and $ 1- 2x + 4x^2 = 64$, then the value of $1 + 2x + 4x^2 $ is :

6 8 12 10

8

We know that, x4 + x2y2 + y4 = (x2 – xy + y2) (x2 + xy + y2) If $ 1 + 4x^2 + 16x^4 = 512 $, $ 1- 2x + 4x^2 = 64$ then the value of $1 + 2x + 4x^2 $ = \(\frac{512}{64}\) = 8