初中数学题库八年级6.4：二次根式中完全平方公式的运用技巧案例解析
原式\(\displaystyle =\frac{{1+\sqrt[4]{3}}}{{\left( {1-\sqrt[4]{3}} \right)\left( {1+\sqrt[4]{3}} \right)}}+\frac{{1-\sqrt[4]{3}}}{{\left( {1-\sqrt[4]{3}} \right)\left( {1+\sqrt[4]{3}} \right)}}+\frac{1}{{1+\sqrt{3}}}\)
\(\displaystyle =\frac{{1+\sqrt[4]{3}}}{{1-\sqrt{3}}}+\frac{{1-\sqrt[4]{3}}}{{1-\sqrt{3}}}+\frac{1}{{1+\sqrt{3}}}\)
\(\displaystyle =\frac{1}{{1-\sqrt{3}}}+\frac{1}{{1+\sqrt{3}}}\)
\(\displaystyle =\frac{{2\left( {1+\sqrt{3}} \right)+2\left( {1-\sqrt{3}} \right)}}{{\left( {1+\sqrt{3}} \right)\left( {1-\sqrt{3}} \right)}}\)
\(\displaystyle =\frac{{-4}}{{1-3}}\)
\(\displaystyle =2\)
原式\(\displaystyle =\left( {5+\sqrt{6}} \right)\sqrt{2}\left( {5-\sqrt{6}} \right)\)
\(\displaystyle =\sqrt{2}\left( {25-6} \right)\)
\(\displaystyle =19\sqrt{2}\)
