If x ≠ y ≠ z & x, y, z are in GP and D = 0, then y is equal to -
Step-by-Step Solution
Key Concept: The determinant D is a Vandermonde-like determinant. For D=0, the rows must be linearly dependent. Given x, y, z are in GP, let x=a, y=ar, z=ar^2. Substituting these into the determinant and simplifying leads to the condition for y.
The determinant is D = |x x^3 x^4-1; y y^3 y^4-1; z z^3 z^4-1|. This can be split into |x x^3 x^4; y y^3 y^4; z z^3 z^4| - |x x^3 1; y y^3 1; z z^3 1|. Given x, y, z are in GP, let x=a, y=ar, z=ar^2. Solving D=0 with these substitutions yields y=2.
Correct Answer: 2