perplexus.info :: Just Math : Rational Resolution

Rational Resolution (Posted on 2016-11-18)

Determine all possible rational solutions to this system of equations:

A + 1/B = 2, and:
B + C*A = 9.7, and:
C + A/B = 5.14

Prove that there are no others.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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a start

| Comment 1 of 2

If A is rational then A can be expressed as the ratio of integers (p,q), q<>0.

Plug that value in eq 1 to find B = q/(2q-p), p<>2q.

Then equating the two expressions for C after substituting in eq 2 and 3 gives p*(quadratic in p and q) = 514. Possible values for p are factors of 514, namely 1,2,257,514.

Posted by xdog on 2016-11-19 13:40:47

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