Question

\(D=\frac{\sqrt{7+\sqrt{5}}+\sqrt{7-\sqrt{5}}}{\sqrt{7+2\sqrt{11}}}-\sqrt{3-2\sqrt{2}}\)

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Answer 1

Đặt:   \(A=\frac{\sqrt{7+\sqrt{5}}+\sqrt{7-\sqrt{5}}}{\sqrt{7+2\sqrt{11}}}\)\(>\)\(0\)

=>   \(A^2=\frac{7+\sqrt{5}+2.\sqrt{\left(7+\sqrt{5}\right)\left(7-\sqrt{5}\right)}+7-\sqrt{5}}{7+2\sqrt{11}}\)

            \(=\frac{14+4\sqrt{11}}{7+2\sqrt{11}}\)

             \(=\frac{2\left(7+2\sqrt{11}\right)}{7+2\sqrt{11}}=2\)

=>  \(A=\sqrt{2}\)

\(D=\sqrt{2}-\sqrt{3-2\sqrt{2}}\)

     \(=\sqrt{2}-\sqrt{\left(\sqrt{2}-1\right)^2}\)

     \(=\sqrt{2}-\left(\sqrt{2}-1\right)=1\)