Question

if x y z are in AP then find the value of (x + Y - z) (y + Z - x)

Answer 1

the 3 numbers are in AP .so y=(x+z)/2
(x+y-z)(y+z-x)
(x+(x+z)/2-z)((x+y/2)+z-x)
((2x+x+z-2z)/2)((x+y+2z-2x)/2)
1/4*(3x-z)(2z+y-x).