Question

if x,y,z are in ap then find the value of (x+y-z)(-x+y+z)

Answer 1

d=common difference
x+d=y
x+2d=z

x+y=x+x+d
(x+y-z)=x+x+x+d-x+2d=3x+d-x+2d=2x-d
(-x+y+z)=-x+x+d+x+2d=x+3d
so
(x+y-z) (-x+y+z)=(2x-d) (x+3d)