Nobody answered this? Come on, guys

x² + 1/x² = 4

(x² + 1/x²)² = 4² = 16

but we also know that (x² + 1/x²)² = x� + 2 + 1/x�

so x� + 2 + 1/x� = 16, and x� + 1/x� = 14

In addition to my algebraic method above, you can also always try to gut out an approximation. (This isn't ideal here, since the answers are packed tightly together, but it's a fallback plan on test day.)

If x² + 1/x² = 4, then we know x should be slightly less than 2. (2² + 1/2² = 4.25, which is close).

By that logic, our answer should be slightly less than 2� + 1/(2�). From there, we should have D or E (... and it's a coin flip).