Consider the system { <mtable columnalign="left left" rowspacing=".2em" columnspacin

Jamison Rios

Jamison Rios

Answered question

2022-07-13

Consider the system
{ 1 = A + B = C + D B C
with A , B , C , D positive.
Does the system imply that A D?

Answer & Explanation

Elijah Benjamin

Elijah Benjamin

Beginner2022-07-14Added 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
Esmeralda Lane

Esmeralda Lane

Beginner2022-07-15Added 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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