Final answer:
To find the value of a³ + b³ + c³ - 3abc, first determine the values of a, b, and c. Substituting these values into the formula yields a result of 54. So the answer is D. 54.
Step-by-step explanation:
To find the value of a³ + b³ + c³ - 3abc, we first need to find the values of a, b, and c. From the given equations, we have a + b + c = 8 and ab + bc + ac = 11. Substituting the values a = 3, b = 13, and c = -10 into the equation gives us:
a³ + b³ + c³ - 3abc = (3)³ + (13)³ + (-10)³ - 3(3)(13)(-10) = 27 + 2197 - 1000 - 1170 = 54
Therefore, the value of a³ + b³ + c³ - 3abc is 54. Thus, the correct answer is D. 54.