căn54 +căn2 phần căn3 + 1 + 4 phần căn6 + căn2
2 câu trả lời
`(\sqrt{54}+\sqrt{2})/(\sqrt{3}+1)+(4)/(\sqrt{6}+\sqrt{2})`
`=((\sqrt{54}+\sqrt{2})(\sqrt{3}-1))/((\sqrt{3}+1)(\sqrt{3}-1))+(4(\sqrt{6}-\sqrt{2}))/((\sqrt{6}+\sqrt{2})(\sqrt{6}-\sqrt{2}))`
`=(9\sqrt{2}-3\sqrt{6}+\sqrt{6}-\sqrt{2})/(2)+\sqrt{6}-\sqrt{2}`
`=(8\sqrt{2}-2\sqrt{6})/(2)+\sqrt{6}-\sqrt{2}`
`=(2\sqrt{2}(4-\sqrt{3}))/(2)+\sqrt{6}-\sqrt{2}`
`=\sqrt{2}(4-\sqrt{3})+\sqrt{6}-\sqrt{2}`
`=4\sqrt{2}-\sqrt{6}+\sqrt{6}-\sqrt{2}`
`=3\sqrt{2}`
`\sqrt{54}` `+` `(\sqrt{2})/((\sqrt{3}+1)` `+` `4/(\sqrt{6}+\sqrt{2})`
`=``\sqrt{54}` `+` `(\sqrt{2}(\sqrt{3}-1))/((\sqrt{3}+1)(\sqrt{3}-1))` `+` `[4(\sqrt{6}-\sqrt{2})]/[(\sqrt{6}+\sqrt{2})(\sqrt{6}-\sqrt{2})]`
`=` `3\sqrt{6}` `+` `(\sqrt{2}(\sqrt{3}-1))/(3-1)` `+` `[4(\sqrt{6}-\sqrt{2})]/(6-2)`
`=` `3\sqrt{6}` `+` `(\sqrt{2}(\sqrt{3}-1))/2` `+` `[4(\sqrt{6}-\sqrt{2})]/4`
`=` `3\sqrt{6}` `+` `(\sqrt{2}(\sqrt{3}-1))/2` `+` `[4(\sqrt{6}-\sqrt{2})]/4`
`=` `3\sqrt{6}` `+` `\sqrt{6}` `-` `\sqrt{2}` `+` `(\sqrt{2}(\sqrt{3}-1))/2`
`=` `4\sqrt{6}` `-` `\sqrt{2}` `+` `(\sqrt{2}(\sqrt{3}-1))/2`
`=` `(8\sqrt{6}-2\sqrt{2})/2` `+` `(\sqrt{2}(\sqrt{3}-1))/2`
`=` `(8\sqrt{6}-2\sqrt{2}+\sqrt{6}-\sqrt{2})/2`
`=` `(9\sqrt{6}-3\sqrt{2})/2`