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Jamison Rios 2022-07-13 Answered
Consider the system
{ 1 = A + B = C + D B C
with A , B , C , D positive.
Does the system imply that A D?
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Answers (2)

Elijah Benjamin
Answered 2022-07-14 Author has 10 answers
Yes.
The 1 = A + B has nothing to do with it, but if A + B = C + D, and B C, then C B 0, and so
A = C + D B = D + C B D + 0 = D

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Esmeralda Lane
Answered 2022-07-15 Author has 7 answers
Yes. Suppose for the sake of contradiction that A > D. We know B C, so add these two inequalities, giving A + B > C + D, a contradiction.
Hence A D

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