Question
Wed August 29, 2012 By:

if a,b,c are in AP ,x is the GM between a and b; y is the GM between b and c ; then show that b^2 is the AM between x^2 and y^2

Expert Reply
Wed August 29, 2012
a, b, c are in AP.
So, 2b = a + c
 
x is the GM between a and b.
So, x2 = ab
 
y is the GM between b and c.
So, y2 = bc
 
Now, x2 + y= ab + bc = b(a + c) = 2b2
So, b2 = (x2 + y2)/ 2
 
Hence, b2 is the AM between x2 and y2.
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