perplexus.info :: Just Math : Geometric and Harmonic Harmony

Geometric and Harmonic Harmony (Posted on 2014-12-15)

Find four positive integers A < B < C < D that satisfy both of these conditions:

(i) The geometric mean of A and D is 24, and:
(ii) The harmonic mean of A, B, C and D is 19.2

See The Solution Submitted by K Sengupta

Rating: 5.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

re: solution

| Comment 3 of 5 |

(In reply to solution by Dej Mar)

Dej Mar:

You wrote

120-(A+D) = (B+C)

But I think you meant.

120-(A+D) = (576/B + 576/C).

In any event, it is not clear to me why you conclude that

576/B and 576/C must both be integers.

Posted by Steve Herman on 2014-12-16 12:37:26

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