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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Analytical solution - corrected Comment 7 of 7 |
(In reply to Analytical solution by Federico Kereki)

you say:

Multiplying both results, 4=(16-q^6)/q^2, so q^6-4q^2-16=0. Writing q^2=r we get r^3-4r-16=0 which has a single real root r=2, so if q=2 then p=1+2, and if q=-2, then p=1-2.

correction:

Multiplying both results, 4=(16-q^6)/q^2, so q^6-4q^2-16=0. Writing q^2=r we get    r^3+4r-16=0         which has a single real root r=2, so if q=2 then p=1+2, and if q=-2, then p=1-2.


  Posted by Ady TZIDON on 2007-07-11 07:19:10
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