Prove that one of the elements can't be in the interval ( 0 , 1 )Let be a , b , c ∈ R so that the sum of two of them is never equal to 1. Prove that atleast on of a b a + b − 1 , b c b + c − 1 , c a c + a − 1 can't be in the interval ( 0 , 1 )I aproached it with contradiction, but can't get sth that is not true.

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Prove that one of the elements can&#039;t be in the interval   (  0  ,  1  )Let be   a  ,  b  ,  c  ∈      R   so that the sum of two of them is never equal to   1. Prove that atleast on of             a      b              a      +      b      −      1        ,            b      c              b      +      c      −      1        ,            c      a              c      +      a      −      1       can&#039;t be in the interval   (  0  ,  1  )I aproached it with contradiction, but can&#039;t get sth that is not true.

Jaelynn Cuevas · Accepted Answer

Let   0  &amp;lt;            a      b              a      +      b      −      1        &amp;lt;  1,   0  &amp;lt;            a      c              a      +      c      −      1        &amp;lt;  1 and   0  &amp;lt;            b      c              b      +      c      −      1        &amp;lt;  1Hence,   0  &amp;lt;                    a        2                    b        2                    c        2                            ∏                  c          y          c                    (      a      +      b      −      1      )        &amp;lt;  1In another hand,   0  &amp;lt;  1  −            a      b              a      +      b      −      1        &amp;lt;  1,   0  &amp;lt;  1  −            a      c              a      +      c      −      1        &amp;lt;  1  and   0  &amp;lt;  1  −            b      c              b      +      c      −      1        &amp;lt;  1, which gives  0  &amp;lt;            (      1      −      a      )      (      b      −      1      )              a      +      b      −      1        &amp;lt;  1,   0  &amp;lt;            (      1      −      c      )      (      a      −      1      )              a      +      c      −      1        &amp;lt;  1,  and   0  &amp;lt;            (      1      −      b      )      (      c      −      1      )              b      +      c      −      1        &amp;lt;  1, which gives  0  &amp;lt;            −              ∏                  c          y          c                    (      a      −      1              )        2                            ∏                  c          y          c                    (      a      +      b      −      1      )        &amp;lt;  1, which is a contradiction.

Prove that one of the elements can't be in the interval ( 0 , 1 ) Let be a

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