SOLUTION: If a^2,b^2,c^2 are in A.P,show that b+c,c+a,a+b are in H.P.

Question 1083840: If a^2,b^2,c^2 are in A.P,show that b+c,c+a,a+b are in H.P.
Answer by ikleyn(52802) (Show Source): You can put this solution on YOUR website!
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This statement is wrong.

I will prove it by presenting a counter-example.


Let a = 1, b = 2, c = .

Then  = 1,   = 4  and   = 7  make an AP.


Now,  b+c = ,  c+a =   and  a+b =  = 3.

But these b+c, c+a and a+b DO NOT MAKE a GP.


To see it, compare the ratios   and .

We have   =  = 

   and    = ,


and these two fractions/expressions    and    are not equal numbers, as you can easily check.

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Comment from student: We have to prove that it is in H.P not in G.P
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My response: Sorry, my error.
Disregard my post.

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