 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  A Reciprocal And Square Problem (Posted on 2007-07-10) Find all real pairs (p, q) satisfying the following system of equations:
ĀĀĀĀ ĀĀĀĀ ĀĀĀĀĀ ĀĀĀĀĀ p - 1/p - q2 = 0

ĀĀĀĀ ĀĀĀĀ ĀĀĀĀĀ ĀĀĀĀĀ 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=üŃ2 then p=1+üŃ2, and if q=-üŃ2, then p=1-üŃ2.

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=üŃ2 then p=1+üŃ2, and if q=-üŃ2, then p=1-üŃ2.

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

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