perplexus.info :: Just Math : Take Third Degree, Solve For Real

Take Third Degree, Solve For Real (Posted on 2007-06-27)

Determine all possible real pairs (p, q) satisfying:

2q³ – p³ = pq²+ 11

See The Solution Submitted by K Sengupta

Rating: 3.0000 (2 votes)

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Factoring Idea

| Comment 2 of 4 |

Start by rearranging the equation as:
(q^3 - p^3) + (q^3 - p*q^2) = 11.
It is then easy to factor as:
(q-p)*(2q^2 + qp + p^2) = 11.

Posted by Brian Smith on 2007-06-27 23:39:53

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