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Question

Let a,b,c be such that b(a+c)0.
If ∣ ∣aa+1a1bb+1b1cc1c+1∣ ∣+∣ ∣ ∣a+1b+1c1a1b1c+1(1)n+2a(1)n+1b(1)nc∣ ∣ ∣=0,

then the value of n is 

 


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

The correct option is C any even integer
We know |A|=|AT|
Transpose the second matrix and then C2C3,C2C1, we get  

∣ ∣aa+1a1bb+1b1cc1c+1∣ ∣∣ ∣ ∣(1)n+2aa+1a1(1)n+1bb+1b1(1)ncc1c+1∣ ∣ ∣=0

So, if n is even, then the equation holds true.

Mathematics

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