Answer:
52
Step-by-step explanation:
1. We see if we cube both sides of the second equation, then it looks more similar to the first equation (E = x^3 + 1/x^3)
(1/x + x)^3 = 4^3
1/x^3 + 3/x + 3x + x^3 = 64
2. Now we rearrange, because we see x^3 + 1/x^3 in the first equation in this equation
x^3 + 1/x^3 + 3x + 3/x = 64
3. We look at 3x + 3/x and see that it looks like the second equation, so we try factoring it
x^3 + 1/x^3 + 3(x + 1/x) = 64
we know x + 1/x = 4, so 3(x + 1/x) = 12
x^3 + 1/x^3 +12 = 64
4. Now we subtract and get our answer
x^3 + 1/x^3 = 52
