Final answer:
To find the value of a^4+1/a^4, square the equation 4=a+a^-1. Rearrange the resulting equation to get a^2+1/a^2=14. Square that equation to get a^4+2+1/a^4=196. Subtract 2 from both sides to find a^4+1/a^4=194.
Step-by-step explanation:
To find the value of a4 + 1/a4, we can start by squaring the equation 4 = a + 1/a. This gives us 16 = a2 + 2 + 1/a2. We can then rearrange this equation to get a2 + 1/a2 = 14. Squaring this equation again, we get a4 + 2 + 1/a4 = 196. Subtracting 2 from both sides, we find that a4 + 1/a4 = 194. Therefore, the value of a4 + 1/a4 is 194.