回復 1# P78961118 的帖子
\(\begin{align}
& {{b}^{3}}=-18\sqrt{3}+14\sqrt{5}>0 \\
& b>0 \\
& \\
& a=b+2\sqrt{3} \\
& {{\left( b+2\sqrt{3} \right)}^{2}}b=2\sqrt{3}+2\sqrt{5} \\
& {{b}^{3}}+4\sqrt{3}{{b}^{2}}+12b=2\sqrt{3}+2\sqrt{5} \\
& \left( -18\sqrt{3}+14\sqrt{5} \right)+4\sqrt{3}{{b}^{2}}+12b-\left( 2\sqrt{3}+2\sqrt{5} \right)=0 \\
& \sqrt{3}{{b}^{2}}+3b-\left( 5\sqrt{3}-3\sqrt{5} \right)=0 \\
& b=\frac{-3+\sqrt{69-12\sqrt{15}}}{2\sqrt{3}}=\sqrt{5}-\sqrt{3} \\
& a=\sqrt{5}+\sqrt{3} \\
& {{\left( a+b \right)}^{6}}={{\left( 2\sqrt{5} \right)}^{6}}=8000 \\
\end{align}\)
