Let a,b,c be positive real numbers such that abc\equal{}\frac{9}{4}. Prove the inequality:
a^3 \plus{} b^3 \plus{} c^3 > a\sqrt {b \plus{} c} \plus{} b\sqrt {c \plus{} a} \plus{} c\sqrt {a \plus{} b}
Jury's variant:
Prove the same, but with abc\equal{}2 inequalitiesinequalities proposed