回復 1# shmilyho 的帖子
\(\begin{align}
& x=\sqrt[3]{7+\sqrt{50}},y=\sqrt[3]{7-\sqrt{50}} \\
& {{x}^{3}}+{{y}^{3}}=14 \\
& xy=-1 \\
& {{\left( x+y \right)}^{3}}={{x}^{3}}+{{y}^{3}}+3xy\left( x+y \right) \\
& {{\left( x+y \right)}^{3}}=14-3\left( x+y \right) \\
& let\ x+y=t \\
& {{t}^{3}}=14-3t \\
& {{t}^{3}}+3t-14=0 \\
& \left( t-2 \right)\left( {{t}^{2}}+2t+7 \right)=0 \\
& {{t}^{2}}+2t+7>0 \\
& t=2 \\
\end{align}\)
