Question

if x y z are in a.p show that (x+2y-z)(2 y+z xz+x-y)=4xyz

Answer 1

Since x,y,z are in AP.

Therefore,

d=y-x

=z-y

=(z-x)/2

(x+2y-z)

=x+y+y-z

=x+y-(z-y)

=x+y-(y-x)

=x+y-y+x

= 2x

(2y+z-x)=

2y+2z-2y

=2z.

{ (z-x)/2=z-y => z-x=2z-2y }

(z+x-y)

=z-(y-x)

=z-(z-y)

=z-z+y

=y

(x+2y-z)(2y+z-x)(z+x-y)

=2x × 2z × y

=4xyz

Hence proved.

Answer 2

Answer:

.....

Step-by-step explanation:

Since x,y,z are in AP.

Therefore,

d=y-x=z-y=(z-x)/2

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

(2y+z-x)=2y+2z-2y =2z. { (z-x)/2=z-y => z-x=2z-2y }

(z+x-y)=z-(y-x)=z-(z-y)=z-z+y =y

(x+2y-z)(2y+z-x)(z+x-y)=2x × 2z × y=4xyz

Hence proved.

hope this helps you ❤️