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If the system of equations C 3 n x + C 4 n y + 35 z = 0 , C 4 n x + 35 y + C 3 n z = 0 and 35 x + C 3 n y + C 4 n z = 0 has a non-trivial solution, then the value of n is equal to ∀ n ∈ N , n ≥ 4

Options

  1. A6
  2. B7
  3. C8
  4. D9

Correct answer

B. 7

Step-by-step solution

For non trival solution, ∆ = 0 C 3 n C 4 n 35 C 4 n 35 C 3 n 35 C 3 n C 4 n = 0 ⇒ C 3 n + C 4 n + 35 = 0 (not possible) or C n 3 = C n 4 = 35 ⇒ n = 7

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