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A Reciprocal And Square Problem (Posted on 2007-07-10) Difficulty: 2 of 5
Find all real pairs (p, q) satisfying the following system of equations:
                      p - 1/p - q2 = 0

                      q/p + pq = 4

See The Solution Submitted by K Sengupta    
Rating: 3.5000 (2 votes)

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re: Solution | Comment 2 of 7 |
(In reply to Solution by Praneeth)

Using the values given for p and q in all combinations, I get the following values:

         p                  q              p - 1/p + q^2       q/p + pq 
-2.825993776082988 -1.572302755514847  -4.944271909999159   4.999689428353011
 .3538578210834085 -1.572302755514847  -4.944271909999159  -4.999689428353011
-.3538578210834085 -1.572302755514847   0                   4.999689428353011
 2.825993776082988 -1.572302755514847   0                  -4.999689428353011
-2.825993776082988  1.572302755514847  -4.944271909999159  -4.999689428353011
 .3538578210834085  1.572302755514847  -4.944271909999159   4.999689428353011
-.3538578210834085  1.572302755514847   0                  -4.999689428353011
 2.825993776082988  1.572302755514847   0                   4.999689428353011
from
                                                           
DEFDBL A-Z
CLS
FOR a = -1 TO 1 STEP 2
FOR b = -1 TO 1 STEP 2
FOR c = -1 TO 1 STEP 2
 q = a * SQR(2 * (SQR(5) - 1))
 p = b * (SQR(5) - 1) + c * SQR(7 - 2 * SQR(5))
 PRINT p; TAB(20); q; TAB(40); p - 1 / p - q * q; TAB(60); q / p + p * q
NEXT
NEXT
NEXT
 

While there are some zeros for the first formula, none of the second produces a 4.

                                                          


  Posted by Charlie on 2007-07-10 11:08:38
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