If-x-y-z-are-pth-qth-and-rth-terms-respectively-of-an-AP-and-also-of-GP-then-x-y-z-y-z-x-z-x-y-is-equal-to-

Question Number 16707 by myaoo5678 last updated on 25/Jun/17

If x, y, z are p th, q th and r th terms respectively,

of an AP and also of GP, then

x^{y - z} y^{z - x} z^{x - y} is equal to

Answered by Tinkutara last updated on 25/Jun/17

x - y = y - z

and 2 y = x + z \Rightarrow z - x = 2 (y - x)

Also y^{2} = x z

x^{x - y} z^{x - y} y^{2 (y - x)} = {(x z)}^{x - y} y^{2 (y - x)}

= y^{2 (x - y)} y^{2 (y - x)} = y^{0} = 1

Commented by myaoo5678 last updated on 26/Jun/17

t h a n k s a l o t S i r .