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AP EAMCET2010MathematicsDeterminants

If | array ccc x & x^2 & 1+x^3 y & y^2 & 1+y^3 z & z^2 & 1+z^3 array |=0, x y z then 1+x y z is equal to

Options

  1. A0
  2. B-1
  3. C1
  4. D2

Correct answer

A. 0

Step-by-step solution

| array lll x & x^2 & 1+x^3 y & y^2 & 1+y^3 z & z^2 & 1+z^3 array |=0, x y z | array lll x & x^2 & 1 y & y^2 & 1 z & z^2 & 1 array |+ | array lll x & x^2 & x^3 y & y^2 & y^3 z & z^2 & z^3 array |=0 | array lll x & x^2 & 1 y & y^2 & 1 z & z^2 & 1 array |+ | array lll 1 & x & x^2 1 & y & y^2 1 & z & z^2 array | x y z=0C₁ C₂ and C₂ C₃ | array lll x & x^2 & 1 y & y^2 & 1 z & z^2 & 1 array |+ | array ccc x & x^2 & 1 y & y^2 & 1 z & z^2 & 1 array | x y z=0(1+x y z) | array lll x & x^2 & 1 y & y^2 & 1 z & z^2 & 1 array |=

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