Có ab+bc+ca≤(a+b+c)23=3⇒23+ab+bc+ca≤133√abc(1+a)(1+b)(1+c)≤13(∑aa+1)=1−∑1a+1≤1−3a+b+c+3=12⇒P≤56Dấu bằng khi a=b=c=1
Có
ab+bc+ca≤(a+b+c)23=3⇒23+ab+bc+ca≤13$\sqrt[3]\frac{abc}{(1+a)(1+b)(1+c)}\le\frac13(\sum_{}^{}\frac a{a+1})=
\frac1
3(3-\sum_{}^{}\frac1{a+1}
)\le1-\frac3{a+b+c+3}=\frac12 $$\Rightarrow P\le\frac56$Dấu bằng khi $a=b=c=1$