# Really, is very large!!!

Here comes the problem,

Let $$a,b,c$$ be real non-negative numbers, prove that:

$$a+b+c\le \frac { { a }^{ 2 }+{ b }^{ 2 } }{ 2c } +\frac { { b }^{ 2 }+{ c }^{ 2 } }{ 2a } +\frac { { c }^{ 2 }+{ a }^{ 2 } }{ 2b } \le \frac { { a }^{ 3 } }{ bc } +\frac { { b }^{ 3 } }{ ca } +\frac { { c }^{ 3 } }{ ab }$$

Note by Isaac Jiménez
3 years, 8 months ago

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Whenever u see cyclic homogeneous inequality. Think of EMV theorem. It helps to prove this ineq in 3lines....

- 3 years, 7 months ago