Proof that a 2 b + b 2 c + c 2 a ≥ a + b + cI've tried getting everything on the left side and transforming it into something squared so that I can prove it's bigger or equals to 0 but I've been unsuccessful.

Question

Proof that             a      2        b    +            b      2        c    +            c      2        a    ≥  a  +  b  +  cI&#039;ve tried getting everything on the left side and transforming it into something squared so that I can prove it&#039;s bigger or equals to 0 but I&#039;ve been unsuccessful.

Cullen Kelly · Accepted Answer

For positives   a,   b and   c by C-S we obtain:      ∑          c      y      c                  a      2        b    ≥                    (                  ∑                      c            y            c                          a        )            2                      ∑                  c          y          c                    b        =            (      a      +      b      +      c              )        2                    a      +      b      +      c        =  a  +  b  +  c  .

Proof that (a^2)/(b) + (b^2)/(c) + (c^2)/(a) >= a+b+c

Answered question

Answer & Explanation

New Questions in Pre-Algebra