\(a=\sqrt{2+\sqrt{2+\sqrt{3}}}-\sqrt{3}.\sqrt{2-\sqrt{2+\sqrt{3}}}\)
\(a^2=8-2\sqrt{2+\sqrt{3}}-2\sqrt{3}\sqrt{2-\sqrt{3}}\)
\(=8-\sqrt{2}\left(\sqrt{4+2\sqrt{3}}\right)-\sqrt{6}.\sqrt{4-2\sqrt{3}}\)
\(=8-\sqrt{2}\left(\sqrt{3}+1\right)-\sqrt{6}\left(\sqrt{3}-1\right)\)
\(=8-\sqrt{6}-\sqrt{2}-3\sqrt{2}+\sqrt{6}\)
\(=8-4\sqrt{2}\)
\(\Rightarrow4\sqrt{2}=8-a^2\)
\(\Rightarrow32=\left(8-a^2\right)^2=a^4-16a^2+64\)
\(\Rightarrow a^4-16a^2+32=0\)
\(a\) là nghiệm của pt trên
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