If x ≠ y ≠ z & x, y, z are in A.P. and D = 0, then 2xy^2z + x^2z^2 is equal to-
Step-by-Step Solution
Key Concept: The determinant D is given by the Vandermonde-like structure. For x, y, z in A.P., let y = x+d, z = x+2d. Setting D=0 and simplifying the expression 2xy^2z + x^2z^2 leads to the value 1.
Given D = |x x^3 x^4-1; y y^3 y^4-1; z z^3 z^4-1| = 0. 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| = 0. Since x, y, z are in A.P., the condition D=0 simplifies to the required expression evaluating to 1.
Correct Answer: A