Ta có
\(A=\sqrt{6+2\sqrt{8\sqrt{3}-10}}-\sqrt{7-\sqrt{3}}\)
=> \(A^2=13+2\sqrt{8\sqrt{3}-10}-\sqrt{3}-2\sqrt{\left(6+2\sqrt{8\sqrt{3}-10}\right)\left(7-\sqrt{3}\right)}\)
=> \(A^2=13+2\sqrt{8\sqrt{3}-10}-\sqrt{3}-2\sqrt{42-6\sqrt{3}+2\sqrt{\left(8\sqrt{3}-10\right)\left(7-\sqrt{3}\right)^2}}\)
=> \(A^2=13+2\sqrt{8\sqrt{3}-10}-\sqrt{3}-2\sqrt{42-6\sqrt{3}+2\sqrt{\left(8\sqrt{3}-10\right)\left(52-14\sqrt{3}\right)}}\)
=> \(A^2=13+2\sqrt{8\sqrt{3}-10}-\sqrt{3}-2\sqrt{\left(\sqrt{52-14\sqrt{3}}-\sqrt{8\sqrt{3}-10}\right)^2}\)
=> \(A^2=13+2\sqrt{8\sqrt{3}-10}-\sqrt{3}-2\left(\sqrt{52-14\sqrt{3}}+\sqrt{8\sqrt{3}-10}\right)\)
=>\(A^2=13-\sqrt{3}-2\sqrt{49-14\sqrt{3}+3}\)
=>\(A^2=13-\sqrt{3}-2\left(7-\sqrt{3}\right)=\sqrt{3}-1\)
=> \(A=\sqrt{\sqrt{3}-1}\)
Vậy \(A=\sqrt{\sqrt{3}-1}\)
Xin lỗi có vài dòng dài nên nó bị chuyển xuống dưới , bạn hiểu hộ mình nhé
