Ta có: \(X=\sqrt{6-3\sqrt{2+\sqrt{3}}}-\sqrt{2+\sqrt{2+\sqrt{3}}}\)
<=> \(X^2=6-3\sqrt{2+\sqrt{3}}+2+\sqrt{2+\sqrt{3}}-2\sqrt{3}.\sqrt{4-\left(2+\sqrt{3}\right)}\)
<= \(X^2=8-2\sqrt{2+\sqrt{3}}-2\sqrt{3}.\sqrt{2-\sqrt{3}}\)
<=> \(X^2=8-\sqrt{2}\left(\sqrt{3}+1\right)-\sqrt{6}\left(\sqrt{3}-1\right)\)
<=> \(X^2=8-4\sqrt{2}\)
<=> \(X^2-8=-4\sqrt{2}\)
=> \(X^4-16X+64=32\)
<=> \(X^4-16X^2+32=0\)
Vậy X là nghiệm phương trình \(X^4-16X^2+32=0\)