761731
`a^3 b^3+b^3 c^3 +c^3 a^3 =3 a^2 b^2 c^2`
`⇔(ab)^3+(bc)^3+(ca)^3+3.ab.bc.ac`
áp dụng hằng đẳng thức 12
`⇒`\(\left[ \begin{array}{l}ab=bc=ac\\ab+bc+ac=0\end{array} \right.\)
`⇒`\(\left[ \begin{array}{l}a=b=c\\ab+bc+ac=0\end{array} \right.\)
`th1 a=b=c`
`⇒T=(a/b+1)(b/c+1)(c/a+1)=(1+1)(1+1)(1+1)=2.2.2=8`
`th2`
`ab+bc+ac=0`
`⇔a^2=(a+b)(a+c)`
`T=(a/b+1)(b/c+1)(c/a+1)=((a+b)(b+c)(c+a))/(abc)=(a^2(b+c))/(abc)=(ac+ab)/(bc)=(ab+bc+ac)/(bc)-1=0-1=-1`