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`