Question

a,b,c are positive real numbers with abc=1
Prove:
1/(a^3+b^3+1)+1/(b^3+c^3+1)+1/(a^3+c^3+1) ≤1

Answer 1

Prove \[\frac{ 1 }{ c^3+b^3+1 }+\frac{ 1 }{b^3+a^3+1 }+\frac{ 1 }{ a^3+c^3+1 }\le1\]