Determine all possible triplet(s) (a, b, c) of positive real numbers, with a ≤ b ≤ c, that satisfy the following system of equations:

a³ – 3a = b, and:

b³ – 3b = c, and:

c³ – 3c = a

(In reply to Analytic solution by Daniel)

Otherwise

 a                b                c   
0.2410733605106 -0.7092097740851  1.7709120513064
0.4450418679126 -1.2469796037175  1.8019377358048
0.7092097740851 -1.7709120513064 -0.2410733605106 *
0.8677674782351 -1.9498558243636 -1.5636629649361 * 
1.1361294934623 -1.9418836348521 -1.4970214963422 *
1.2469796037175 -1.8019377358048 -0.4450418679126 *
1.4970214963422 -1.1361294934623  1.9418836348521
1.5636629649361 -0.8677674782351  1.9498558243636
1.7709120513064  0.2410733605106 -0.7092097740851
1.8019377358048  0.4450418679126 -1.2469796037175
1.9418836348521  1.4970214963422 -1.1361294934623
1.9498558243636  1.5636629649361 -0.8677674782351
2.0000000000000  2.0000000000000  2.0000000000000 *

though only those marked * can be cycled into an ascending series.

 

Posted by Charlie on 2009-05-16 17:04:01