rút gọn A= ((1/3 - căn 5)-(1/3+căn 5)) : căn 5

2 câu trả lời

`#tnvt`

`A=[\frac{1}{3-\sqrt{5}}-\frac{1}{3+\sqrt{5}}]:\sqrt{5}`

`=[\frac{3+\sqrt{5}}{(3-\sqrt{5})(3+\sqrt{5})}-\frac{3-\sqrt{5}}{(3-\sqrt{5})(3+\sqrt{5})}]:\sqrt{5}`

`=[\frac{3+\sqrt{5}-(3-\sqrt{5})}{3^2-\sqrt{5}^2}]:\sqrt{5}`

`=[\frac{3+\sqrt{5}-3+\sqrt{5}}{9-5}].\frac{1}{\sqrt{5}}`

`=\frac{2\sqrt{5}}{4}.\frac{1}{\sqrt{5}}`

`=\frac{\sqrt{5}}{2}.\frac{1}{\sqrt{5}}`

`=\frac{\cancel{\sqrt{5}}}{2}.\frac{1}{\cancel{\sqrt{5}}}`

`=1/2`

Đáp án + Giải thích các bước giải:

`A` `=` `(1/(3-\sqrt{5}) - 1/(3+\sqrt{5}))` `:` `\sqrt{5}`

`=` `[ (3+\sqrt{5})/((3-\sqrt{5})(3+\sqrt{5})) - (3-\sqrt{5})/((3-\sqrt{5})(3+\sqrt{5})) ]` `.` `1/\sqrt{5}`

`=` `[ (3+\sqrt{5})/4 - (3-\sqrt{5})/4 ]` `.` `1/\sqrt{5}`

`=` `(3+\sqrt{5}-3+\sqrt{5})/4` `.` `1/\sqrt{5}`

`=` `(2\sqrt{5})/4` `.` `1/\sqrt{5}`

`=` `2/4` `=` `1/2`