Đáp án:
Giải thích các bước giải:
`sqrt{(2+sqrt3)/(2-sqrt3)} + sqrt{(2-sqrt3)/(2+sqrt3)}`
`= sqrt{((2+sqrt3)(2+sqrt3))/((2-sqrt3)(2+sqrt3))} + sqrt{((2-sqrt3)(2-sqrt3))/((2+sqrt3)(2-sqrt3))}`
`= sqrt{((2+sqrt3)(2+sqrt3))/(2^2-(sqrt3)^2)} + sqrt{((2-sqrt3)(2-sqrt3))/(2^2-(sqrt3)^2)}`
`= sqrt{(2+sqrt3)(2+sqrt3)} + sqrt{(2-sqrt3)(2-sqrt3)}`
`= sqrt{(2+sqrt3)^2} + sqrt{(2-sqrt3)^2}`
`= |2 + sqrt3| + |2 - sqrt3|`
`= 2 + sqrt3 + 2 - sqrt3`
`= 4`
*Áp dụng hằng đẳng thức :
`(a+b)(a-b) = a^2 - b^2`
`sqrt{A^2} = |A|`
