$$\left. \begin{array} { l } { a + c \quad b + c \quad a + b + c } \\ { c ^ { 4 } - 2 ( a ^ { 2 } + b ^ { 2 } ) c ^ { 2 } + a ^ { 4 } + a ^ { 2 } b ^ { 2 } + b ^ { 4 } = 0 , C = 60 ^ { \circ } \right.$$
$c=-\sqrt{a^{2}-ab+b^{2}}\text{, }a\in \mathrm{R}\text{, }b\in \mathrm{R}\text{, }C=60\text{, }d=-a\sqrt{a^{2}-ab+b^{2}}-b\sqrt{a^{2}-ab+b^{2}}-\sqrt{a^{2}-ab+b^{2}}+a+b$
$c=\sqrt{a^{2}-ab+b^{2}}\text{, }a\in \mathrm{R}\text{, }b\in \mathrm{R}\text{, }C=60\text{, }d=a\sqrt{a^{2}-ab+b^{2}}+b\sqrt{a^{2}-ab+b^{2}}+\sqrt{a^{2}-ab+b^{2}}+a+b$
$c=-\sqrt{a^{2}+ab+b^{2}}\text{, }a\in \mathrm{R}\text{, }b\in \mathrm{R}\text{, }C=60\text{, }d=-a\sqrt{a^{2}+ab+b^{2}}-b\sqrt{a^{2}+ab+b^{2}}-\sqrt{a^{2}+ab+b^{2}}+a+b$
$c=\sqrt{a^{2}+ab+b^{2}}\text{, }a\in \mathrm{R}\text{, }b\in \mathrm{R}\text{, }C=60\text{, }d=a\sqrt{a^{2}+ab+b^{2}}+b\sqrt{a^{2}+ab+b^{2}}+\sqrt{a^{2}+ab+b^{2}}+a+b$
