Question
Fri March 23, 2012 By:

If 1/y+z, 1/z+x, 1/x+y are in AP Then show that ?x^2 y^2 z?^2 in AP Sir/ Madam . which you solved is not solved in AP formula wise i feel. if so can u plz explain me thank u

Expert Reply
Fri March 23, 2012
This question has being solved using the concept of AP only.
 
Since, 1/y+z, 1/z+x, 1/x+y are in AP, therefore the common difference will be the same. Hence, we have: 

1/x+z - 1/y+z = 1/x+y - 1/z+x

So taking LCM, we get, y-x / y+z = z-y / x+y

On cross multiplying we get ,

x2 + z2 = 2y2

y2 - x2 = z2 - y2 

Hence, x2, y2, z2 are in AP.  

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