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 a Vandermonde-like determinant. Given x, y, z are in A.P., we can substitute y = (x+z)/2. Since D=0 and x, y, z are distinct, the expression simplifies based on the properties of the determinant.
The determinant D = (x-y)(y-z)(z-x)(xy+yz+zx+1). Given D=0 and x, y, z are distinct, we must have xy+yz+zx+1=0. Since x, y, z are in A.P., y = (x+z)/2. Substituting this into the condition and solving for the expression 2xy^2z + x^2z^2 leads to the result 1.
Correct Answer: 1