Show that if b^2 is the arithmetic mean of a^2 and c^2, then 1/(c+a) is the arithmetic mean of 1/(b+c) and 1/(a+b). Assume a^2 is not equal to c^2. Can someone give me a hint to send me in the right direction.

Question

anonymous · Answer

I'm going out to enjoy what's left of the day and I'll come back to this later tonight.

anonymous · Answer

1/(c+a) will be Arithmetic  mean of 1/(b+c) and 1/(a+b)
if $$2*\frac{ 1 }{ c+a }=\frac{ 1 }{ b+c }+\frac{ 1 }{ a+b }$$
$$if~\frac{ 2 }{ c+a }=\frac{ a+b+b+c }{ \left( b+c \right)\left( a+b \right) }$$
cross multiply and simplify

anonymous · Answer

Thank you so much