回復 1# lungxo 的帖子
\(\begin{align}
& a+b=-\left( c+d \right) \\
& \\
& {{a}^{3}}+{{b}^{3}}+{{c}^{3}}+{{d}^{3}} \\
& ={{\left( a+b \right)}^{3}}-3ab\left( a+b \right)+{{\left( c+d \right)}^{3}}-3cd\left( c+d \right) \\
& =3ab\left( c+d \right)-3cd\left( c+d \right) \\
& =3\left( c+d \right)\left( ab-cd \right) \\
& =3\left[ abc+abd-cd\left( c+d \right) \right] \\
& =3\left[ abc+abd+cd\left( a+b \right) \right] \\
& =3\left( abc+abd+acd+bcd \right) \\
& \\
& abc+abd+acd+bcd=\frac{5}{3} \\
\end{align}\)
