Question

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Answer 1

\(\sqrt{2}A=\sqrt{10-2.\sqrt{7}.\sqrt{3}}+\sqrt{10+2.\sqrt{7}.\sqrt{3}}\)

\(=\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{7}+\sqrt{3}\right)^2}\)

\(=\sqrt{7}-\sqrt{3}+\sqrt{7}+\sqrt{3}=2\sqrt{7}\)

\(\Rightarrow A=\frac{2\sqrt{7}}{\sqrt{2}}=\sqrt{14}\)

Answer 2

Có  :\(2A=\sqrt{10+2\sqrt{21}}+\sqrt{10-2\sqrt{21}}\)

             \(=\sqrt{\left(\sqrt{7}+\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}\)

             \(=\sqrt{7}+\sqrt{3}+\sqrt{7}-\sqrt{3}=2\sqrt{7}\)

=> \(A=\frac{2\sqrt{7}}{2}=\sqrt{7}\)