Question

If x,y,z are in A.P .,then find the value of (x+y+z)(y+z-x)

Answer 1

The answer isif x , y and z are in A.P 

then 

y = (x+z)/2 

substitute this for y 

(x+ (x+z)/2 - z) ( (x+z)/2 +z -x) 

( 2x +x +z -2z) /2 * ( x+z +2z -2x ) /2 
1/4 * (3x-z)(3z -x)