Let a, b, and c be positive real numbers such that a + b + c = 1. Find the minimum value of (1/a + 1/b + 1/c).
Correct: C
By Cauchy-Schwarz inequality, (a + b + c)(1/a + 1/b + 1/c) >= (1 + 1 + 1)^2 = 9. Since a + b + c = 1, we have 1 * (1/a + 1/b + 1/c) >= 9, so (1/a + 1/b + 1/c) >= 9. Equality holds when a = b = c = 1/3, which gives 1/a + 1/b + 1/c = 3 + 3 + 3 = 9.