perplexus.info :: Just Math : Three Equation System Settlement

Three Equation System Settlement (Posted on 2016-10-07)

Find all possible real number solutions to this system of equations:

A+B*C = B+C*A = C+A*B = 1980

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

d2? (spoiler)

| Comment 1 of 5

Consider the first equality,

A + BC = B+CA

Solving for C, we find C = (A-B)/(A-B).

Since (1,1,1) is not a solution, it must be the case that A=B=C

Then A^2 +A - 1980 = 0

The square root of 1980 is about 44.5,

so (A+45)(A-44) = 0

Solutions are (-45, -45, -45) and (44,44,44)

Posted by Steve Herman on 2016-10-07 14:07:41

Please log in:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (14)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info