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Question

If ∣∣ ∣∣aa+1a−1−bb+1b−1cc−1c+1∣∣ ∣∣+∣∣ ∣ ∣∣a+1b+1c−1a−1b−1c+1(−1)n+2a(−1)n+2b(−1)nc∣∣ ∣ ∣∣=0. Then the value of n is

A
zero
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B
any even integer
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C
any odd integer
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D
any integer
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Solution

The correct option is C any integer
∣ ∣ ∣a+1b+1c1a1b1c+1(1)n+2a(1)n+2b(1)nc∣ ∣ ∣=∣ ∣222a1b1c+1(1)na(1)nb(1)nc∣ ∣=2(1)n∣ ∣111a1b1c+1abc∣ ∣ =2(1)n∣ ∣111abcabc∣ ∣=0
n is any integer

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