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Some Reals Sum Two (Posted on 2008-09-01) Difficulty: 3 of 5
Determine all possible real quadruplet(s) (P, Q, R, S) with P ≤ Q ≤ R ≤ S that satisfy this system of equations:

P + Q*R*S = 2, and:

Q + R*S*P = 2, and:

R + P*Q*S = 2, and:

S + P*Q*R = 2.

  Submitted by K Sengupta    
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Solution: (Hide)
(P,Q,R,S) = (1,1,1,1) and (-1,-1,-1,3).

EXPLANATION:

Refer to the methodologies submitted by Daniel and Steve Herman in the first two comments.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(2): Unreal!Steve Herman2008-09-01 20:02:20
Questionre: Unreal!Ady TZIDON2008-09-01 17:48:00
Some ThoughtsUnreal!Steve Herman2008-09-01 15:23:28
re: solution checkingDaniel2008-09-01 14:21:20
solution checkingSteve Herman2008-09-01 14:06:10
Solutionsolution (spoiler)Daniel2008-09-01 13:06:26
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