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If |[x^n, x^(n+2),x^(n+3)],[y^n, y^(n+2)...

If `|[x^n, x^(n+2),x^(n+3)],[y^n, y^(n+2),y^(n+3)],[z^n, z^(n+2),z^(n+3)]|=(x-y)(y-z)(z-x)(1/x+1/y+1/z),` then `n` equals

A

`1`

B

`-1`

C

`2`

D

`-2`

Text Solution

Verified by Experts

The correct Answer is:
B
The degree or each terms of the determinant is `n + (n+2)+ (n+3) =3n+5` and the degree of each terms of the expression on R.H.S. is 2.
`:. 3n+ 5=2 " or " n=-1`
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