Inequality on non-negative realsFor non-negative x , y , z satisfy 1 2 x 2 + 1 + 1 2 y 2 + 1 + 1 2 z 2 + 1 = 1 then show that Idea how to handle the constraint? I'm unaware .

Question

Inequality on non-negative realsFor non-negative   x  ,  y  ,  z satisfy       1          2              x        2            +      1        +      1          2              y        2            +      1        +      1          2              z        2            +      1        =  1 then show that Idea how to handle the constraint? I&#039;m unaware .

Lamont Adkins · Accepted Answer

Yes, it&#039;s true for all reals.      ∑          c      y      c        (      x    2    −  3  x  +  2  )  =      ∑          c      y      c            (          x      2        −    3    x    +    2    −          9      4              (              1                  2                      x            2                    +          1                    −              1        3            )        )    =      ∑          c      y      c                  (      x      −      1              )        2            (      2      x      −      1              )        2                    2      (      2              x        2            +      1      )        ≥  0Done!

Inequality on non-negative reals For non-negative x , y , z satisfy 1

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