Question

If x, y and z are in A.P show that xy+yz =2z2

Answer 1

Question:

If x ,y and z are in AP , then show that

xy + yz = 2y^2

Solution:

Note:

If a , b , c are in AP , then ;

=> b - a = c - b

=> 2b = a + c

Here, it is given that,

x , y , z are in AP

Thus,

=> y - x = z - y

=> 2y = x + z

=> 2y= (x + z)

multiplying both sides by y , we get

=> 2y^2 = xy + yz

Hence proved.