Question

If x y and z are in ap then find the value of (x+y-z)(y+z-x)

Answer 1

Answer:

X,Y,Z are in AP

then y-x=z-y

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

HENCE ,

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