If $ 1 + x^2 + x^4 = 585$ and $ 1 - x + x^2 = 65$, then find the value of $ 1 + x + x^2$.
Answer & explanation
Correct answer: option 4
If $ 1 + x^2 + x^4 = 585$
$ 1 - x + x^2 = 65$,
then find the value of $ 1 + x + x^2$
We know that,
x4 + x2y2 + y4 = (x2 – xy + y2) (x2 + xy + y2)
So, $ 1 + x + x^2$ = \(\frac{585}{65}\) = 9