If <span class="math-tex">\(a_1, a_2, a_3,...,a_n\)</span> are positive real numbers whose product is a fixed number C, then the minimum value of <span class="math-tex">\(a_1+a_2+...+a_n\)</span> is
By the AM–GM inequality:
\(\frac{a_1 + a_2 + \dots + a_n}{n} \ge (a_1 a_2 \cdots a_n)^{1/n} = C^{1/n}\)
So \(a_1 + \dots + a_n \ge nC^{1/n}\). Equality holds when all \(a_i = C^{1/n}\).
Minimum = \(nC^{1/n}\)
Answer: (C)
Reinforce your conceptual grasp with related questions from MAH MCA CET 2018:
Take timed full-length mock tests with authentic question distributions, negative marking (+12/-3 in Math), and instant All India Rank calculation.
Start Free Mock Test Series →