Question

Harmonic mean if a number h such that
(h-a)/(b-h)=a/b

Prove h is H(a,b) iff satisfies either relation
a. (1/a)-(1/h) = (1/h) - (1/b)
b. h = (2ab)/(a+b)

Answer 1

you are saying that h is harmonic mean of a and b ??

Answer 2

Yes, the problem states. that h is the harmonic mean of a and b, where a < b, such that (h-a)/(b-h)= a/b...

it is saying that is true if and only if h satisfies either condition given above

Answer 3

and it wants me to prove that

Answer 4

you know that 1/b , 1/h , 1/a are in arithmetic progression
so that
2/h = 1/a + 1/b

Answer 5

okay. i understand that. so u just saying by showing what is already known from arithmetic, you can just use that to show part a. and split up 1/h + 1/h, and just move around.

Answer 6

yup.. similarly.. take reciprocal of both sides and part b will be proved :)

Answer 7

that doesnt seem like much of a proof... seems like i would just start by stating the arithmetic and move a few things around and poof.. proof finished... and if you prove a... and you use the reciprocal for b, doesnt that mean that a and b is always true if one of them is... idk, i guess it just doesnt seem like much work.

Answer 8

and you are not even using the given equation... do you not have to?

Answer 9

its universal identity for harmonic progressions man

Answer 10

alright... well thank you for your help

Answer 11

welcome =)