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If a , b , c ∈ N and D = a b c c a b b c a , then the least positive value of D is

Options

  1. A4
  2. B6
  3. C3
  4. D8

Correct answer

A. 4

Step-by-step solution

a b c c a b b c a = a 3 × b 3 × c 3 - 3 a b c = a + b + c 2 a - b 2 + b - c 2 + c - a 2 For least positive value, when a , b , c ∈ N, two of them are 1 and one of them is 2 So, D m i n = 4

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