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].

Question

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].

Accepted Answer

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

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].

Solution

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