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For a, b, c > 0 and real x, y, z, evaluate the determinant whose rows are [(a^x + a^-x)², (a^x - a^-x)², 1], [(b^y + b^-y)², (b^y - b^-y)², 1], [(c^z + c^-z)², (c^z - c^-z)², 1].

1. a^x b^y c^z
2. a^-x b^-y c^-z
3. a²x b²y c²z
4. zero

Correct answer: zero

Solution

Column1 minus Column2 equals 4 for every row, a constant multiple of column 3, so the determinant is zero.

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