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KCET2018MathematicsDeterminants

If ( x, y, z R ), then the value of determinant [ | array lll (5^ x +5^ -x )² & (5^ x -5^ -x )² & 1 (6^ x +6^ -x )² & (6^ x -6^ -x )² & 1 (7^ x +7^ -x )² & (7^ x -7^ -x )² & 1 array | is ]

Options

  1. A( 10 )
  2. B( 12 )
  3. C( 11 )
  4. D( 00 )

Correct answer

D. ( 00 )

Step-by-step solution

Given that, ( | array ccc (5^ x +5^ -x )² & (5^ x -5^ -x )² & 1 (6^ x +6^ -x )² & (6^ x -6^ -x )² & 1 (7^ x +7^ -x )² & (7^ x -7^ -x )² & 1 array | ) ( C₁ C₁-C₂ ) ( | array ccc 4 & (5^ x -5^ -x )² & 1 4 & (6^ x -6^ -x )² & 1 4 & (7^ x -7^ -x )² & 1 array |=4 | array ccc 1 & (5^ x -5^ -x )² & 1 1 & (6^ x -6^ -x )² & 1 1 & (7^ x -7^ -x )² & 1 array |=0 )

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