tính giúp mk vs $\sqrt{\frac{2-\sqrt{3}}{2+\sqrt{3}}}$ + $\sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}}$

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1. Đáp án:

   `\sqrt{(2-sqrt3)/(2+sqrt3)}+sqrt{(2+sqrt3)/(2-sqrt3)}`

   `=\sqrt{(4-2sqrt3)/(4+2sqrt3)}+sqrt{(4+2sqrt3)/(4-2sqrt3)}`

   `=sqrt{(3-2sqrt3+1)/(3+2sqrt3+1)}+sqrt{(3+2sqrt3+1)/(3-2sqrt3+1)}`

   `=sqrt{(sqrt3-1)^2/(sqrt3+1)^2}+sqrt{(sqrt3+1)^2/(sqrt3-1)^2}`

   `=|(sqrt3-1)/(sqrt3+1)|+|(sqrt3+1)/(sqrt3-1)|`

   `=(sqrt3-1)/(sqrt3+1)+(sqrt3+1)/(sqrt3-1)`

   `=((sqrt3-1)^2)/((sqrt3+1)(sqrt3-1))+((sqrt3+1)^2)/((sqrt3-1)(sqrt3+1))`

   `=(sqrt3-1)^2/2+(sqrt3+1)^2/2`

   `=((sqrt3-1)^2+(sqrt3+1)^2)/2`

   `=(3-2sqrt3+1+3+2sqrt3+1)/2`

   `=8/2=4`

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