​ If a, b, c are in A.P. and x, y, z are in G.P., then the value of is A. 0 B. 1 C. xyz ​

Question

If a, b, c are in A.P. and x, y, z are in G.P., then the value of \(x^{b-c}, y ^{c-a}, z^{a-b}\) is 

A. 0 

B. 1 

C. xyz

D. X^a Y^b Z^c

Answer 1

Correct answer is B. 1

Given:

a,b,c are in AP and x,y,z are in GP

⇒ 2b = a+c and y² = xz.

⇒ x =  \(\frac{y^2}{z}\)

L.H.S = x^b-c .y^c-a .z^a-b