perplexus.info :: Just Math : Real and Cyclic Sum

Real and Cyclic Sum (Posted on 2016-08-10)

Determine all possible real solutions to this system of equations:

A+B+C+D = 5, and:
A*B+B*C+C*D+D*A = 4, and:
A*B*C+B*C*D+C*D*A+D*A*B= 3, and:
A*B*C*D= -1

Prove that there are no others.

Submitted by K Sengupta

Rating: 4.5000 (2 votes)

Solution: (Hide)

{A, B, C, D} = {(1 + sqrt2)/2, 2, (1 – sqrt2)/2, 2}, {(1 - sqrt2)/2, 2, (1 + sqrt2)/2, 2}, {2, (1 + sqrt2)/2, 2, (1 – sqrt2)/2}, {2, (1 – sqrt2)/2, 2, (1 + sqrt2)/2}
For an explanation, refer to the solution submitted by Harry in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: adding on	Harry	2016-08-12 06:13:25
adding on	xdog	2016-08-11 18:20:34
Possible Solution	Harry	2016-08-11 16:31:53

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