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Demonstrati ca oricare ar fi \( x,y,z \in (-1, \infty) \), are loc inegalitatea
\( \frac{(x+1)^2+yz-1}{y+z+2}+\frac{(y+1)^2+xz-1}{ x+z+2}+\frac{(z+1)^2+xy-1}{x+y+2} \geq x+y+z \).
Claudiu Coanda, Concursul "Ion Ciolac", 2005

Notand x+1=a , y+1=b , z+1=c inegalitatea se reduce la

\( \frac{a^2+bc}{b+c}+\frac{b^2+ca}{c+a}+\frac{c^2+ab}{a+b}\ge a+b+c \)

care este cunoscuta.