Question

giúp với

\(D=\sqrt{\frac{\sqrt{10}+3}{\sqrt{10}-3}}+\sqrt{\frac{\sqrt{10-3}}{\sqrt{10}+3}}\)

 

Answer 1

\(D=\sqrt{\frac{\sqrt{10}+3}{\sqrt{10}-3}}+\sqrt{\frac{\sqrt{10}-3}{\sqrt{10}+3}}\)

     \(=\sqrt{\frac{\left(\sqrt{10}+3\right)\left(\sqrt{10}+3\right)}{\left(\sqrt{10}-3\right)\left(\sqrt{10}+3\right)}}+\sqrt{\frac{\left(\sqrt{10}-3\right)\left(\sqrt{10}-3\right)}{\left(\sqrt{10}+3\right)\left(\sqrt{10}-3\right)}}\)

       =    \(\sqrt{\frac{\left(\sqrt{10}+3\right)^2}{10-9}}+\sqrt{\frac{\left(\sqrt{10}-3\right)^2}{10-9}}\)

     \(=\sqrt{\left(\sqrt{10}+3\right)^2}+\sqrt{\left(\sqrt{10}-3\right)^2}\)

      \(=\sqrt{10}+3+\sqrt{10}-3\) ( Vì \(\sqrt{10}\) lớn hơn \(3\) )

     \(=2\sqrt{10}\)

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