2007 AMC 10A Problem 20

Suppose that the number a satisfies the equation 4 = a + a^{ - 1}. What is the value of a^{4} + a^{ - 4}?

\text{(A)}\ 164 \qquad \text{(B)}\ 172 \qquad \text{(C)}\ 192 \qquad \text{(D)}\ 194 \qquad \text{(E)}\ 212

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.