perplexus.info :: Just Math : Multiplication Quickie

Multiplication Quickie (Posted on 2024-06-21)

Each of a, b, and c is a real number that satisfy:

a-b = a*b*c
b-c = a*b*c
c+a = 3*a*b*c

Using only p&p, how fast can you come up with all possible values of a*c

See The Solution Submitted by K Sengupta

Rating: 4.0000 (2 votes)

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Solution

Comment 2 of 2 |

Start with the linear combination -[a-b = a*b*c] + [b-c = a*b*c] + [c+a = 3*a*b*c]

This yields 2*b = 3*a*b*c. Then either b=0 or a*c=2/3.

If b=0 then a=0 and c=0 as well, so a*c=0 is another possibility.

The total set of possible values of a*c is 0 or 2/3.

Posted by Brian Smith on 2024-06-22 12:45:23

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