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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

Submitted by K Sengupta

Rating: 5.0000 (2 votes)

Solution: (Hide)

The required quadruplets {A,B,C,D) are (8, 24, 36, 72) and (12, 16, 24, 28) as the two possible solutions.
For an explanation, refer to the solution submitted by Dej Mar and the rejoinder by JayDeeKay here and here.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re(3): solution	K Sengupta	2024-03-16 01:07:02
re(2): solution	JayDeeKay	2014-12-22 12:37:34
re: solution	Steve Herman	2014-12-16 12:37:26
solution	Dej Mar	2014-12-15 19:12:55
solution (no proof)	Paul	2014-12-15 16:34:06

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