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Let x, y, z be positive reals and D be the determinant with rows (x, x³, x⁴ - 1), (y, y³, y⁴ - 1), (z, z³, z⁴ - 1). If x, y, z are distinct, are in GP, and D = 0, then y equals:
- 1
- 2
- 4
- none of these
Correct answer: 1
Solution
Splitting the third column and using xyz with GP condition xz = y² leads to xyz = 1 with y² = xz, giving y = 1.
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