Đáp án:
`sqrt{ 1/(3-sqrt{5})+1/(3+sqrt{5}) }:(5-sqrt{5})/(sqrt{5}-1)=sqrt{30}/10`
Giải thích các bước giải:
`sqrt{ 1/(3-sqrt{5})+1/(3+sqrt{5}) }:(5-sqrt{5})/(sqrt{5}-1)`
`=sqrt{(3+sqrt{5})/((3-sqrt{5})(3+sqrt{5}))+(3-sqrt{5})/((3+sqrt{5})(3-sqrt{5}))}:(sqrt{5}.(sqrt{5}-1))/(sqrt{5}-1)`
`=sqrt{(3+sqrt{5})/(9-5)+(3-sqrt{5})/(9-5)}:sqrt{5}`
`=sqrt{(3+sqrt{5})/4+(3-sqrt{5})/4}. 1/sqrt{5}`
`=sqrt{(3+sqrt{5}+3-sqrt{5})/4}. 1/sqrt{5}`
`=sqrt{6/4}. 1/sqrt{5}`
`=sqrt{6}/sqrt{4} . 1/sqrt{5}`
`=sqrt{6}/sqrt{20}`
`=(sqrt{20}sqrt{6})/20`
`=(sqrt{4}.sqrt{5}.sqrt{6})/(2.10)`
`=sqrt{30}/10`
