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If x,y,z are in AP . Prove that (x+2y-z)(2y+z-x)(z+x-y)=4xyz
If x,y,z are in AP . Prove that (x+2y-z)(2y+z-x)(z+x-y)=4xyz

```
3 years ago

```							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=4xyzHence proved.
```
3 years ago
```							hi surajthis is typical application of ideastake x as starter of the series and common difference to be dthen y=x+dz=x+2dtherefore (x+2y-z)=(x+2x+2d-x-2d)=2x(2y+z-x)=(2x+2d+x+2d-x)=2(x+2d)=2z(z+x-y)=(x+2d+x-x-d)=yso product gives u 4xyz
```
3 years ago
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