If $ 1 + 4x^2 + 16x^4 = 512 $, and $ 1- 2x + 4x^2 = 64$, then the value of $1 + 2x + 4x^2 $ is :
Answer & explanation
Correct answer: option 2
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