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Prove that
a+b+c\ge 2\left(\frac{a}{a+1}+\frac{b}{b+1}+\frac{c}{c+1}\right)
holds \forall a,b,c\ge 0: a^3+b^3+c^3+2abc=5.
a+b+c\ge 2\left(\frac{a}{a+1}+\frac{b}{b+1}+\frac{c}{c+1}\right)
holds \forall a,b,c\ge 0: a^3+b^3+c^3+2abc=5.
