tiếp tục nek các bạn ơi

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tranvanhung7997

$A=\sqrt[]{\frac{5+2\sqrt[]{6}}{5-\sqrt[]{6}}}+\sqrt[]{\frac{5-2\sqrt[]{6}}{5+\sqrt[]{6}}}$
Ta có: $A^2=\frac{5+2\sqrt[]{6}}{5-\sqrt[]{6}}+\frac{5-2\sqrt[]{6}}{5+\sqrt[]{6}}+ 2\sqrt[]{\frac{(5+2\sqrt[]{6})(5-2\sqrt[]{6})}{(5-\sqrt[]{6})(5+\sqrt[]{6})}}$
$=\frac{(5+2\sqrt[]{6})(5+\sqrt[]{6})+(5-2\sqrt[]{6})(5-\sqrt[]{6})}{(5+\sqrt[]{6})(5-\sqrt[]{6})}+2\sqrt[]{\frac{25-24}{25-6}}$
$=\frac{(37+15\sqrt[]{6})+(37-15\sqrt[]{6})}{25-6}+\frac{2}{\sqrt[]{19}}$
$=\frac{74}{19}+\frac{2\sqrt[]{19}}{19}$
$=\frac{74+2\sqrt[]{19}}{19}$
\Rightarrow $A=\sqrt[]{\frac{74+2\sqrt[]{19}}{19}}$
 
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