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

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Solution

x, y and z are in the AP.

So, 2y = x + z

x = 2y - z .......(1)

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

Substituting (1) in (2)

[(2y - z) + y - z][y + z - (2y - z)]

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

= (3y - 2z)(2z - y)

= 6yz - 3y2 - 4z2 + 2yz

= 8yx - 3y2 - 4z2

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