Rút gọn: √(11-4 √7) – 3 $\frac{x}{y}$ √7-2

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1. Đáp án + Giải thích các bước giải:

   `sqrt(11-4sqrt(7))-3/(sqrt(7)-2)` 

   `=sqrt(4-2.2sqrt(7)+7)-3/(sqrt(7)-2)`

   `=sqrt((2-sqrt(7))^2)-3/(sqrt(7)-2)`

   `=|2-sqrt(7)|-3/(sqrt(7)-2)`

   `=sqrt(7)-2-3/(sqrt(7)-2)`

   `=((sqrt(7)-2)^2-3)/(sqrt(7)-2)`

   `=(11-4sqrt(7)-3)/(sqrt(7)-2)`

   `=(8-4sqrt(7))/(sqrt(7)-2)`

   `=(4.(2-sqrt(7)))/(sqrt(7)-2)=-(4.(sqrt(7)-2))/(sqrt(7)-2)`

   `=-4`

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2. `sqrt{11 – 4sqrt7} – 3/(sqrt7 – 2)`

   `= sqrt{4 – 4sqrt7 + 7} – 3/(sqrt7 – 2)`

   `= sqrt{2^2 – 2. 2sqrt7 + (sqrt7)^2} – 3/(sqrt7 – 2)`

   `= sqrt{(2 – sqrt7)^2} – 3/(sqrt7 – 2)`

   `= |2 – sqrt7| – 3/(sqrt7 – 2)`

   `= sqrt 7 – 2 – 3/(sqrt7 – 2)`

   `= (sqrt7 – 2)^2/(sqrt7 – 2) – 3/(sqrt7 – 2)`

   `= (11 – 4sqrt7)/(sqrt7 – 2) – 3/(sqrt7 – 2)`

   `= (11 – 4sqrt7 – 3)/(sqrt7 – 2)`

   `= (8 – 4sqrt7)/(sqrt7 – 2)`

   `= – (4sqrt7 – 8)/(sqrt7 – 2)`

   `= -(4(sqrt7 – 2))/(sqrt7 – 2)`

   `= -4`

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