Đáp án:
`h)-4`
`i)2,4`
`j)\sqrt{2}-2-\sqrt{3}`
Giải thích các bước giải:
`h)(1+(\sqrt{5}-5)/(\sqrt{5}-1))(1+(\sqrt{5}+5)/(\sqrt{5}+1))`
`=(1+(-\sqrt{5}(\sqrt{5}-1))/(\sqrt{5}-1))(1+(\sqrt{5}(\sqrt{5}+1))/(\sqrt{5}+1))`
`=(1-\sqrt{5})(1+\sqrt{5})`
`=1^2-(\sqrt{5})^2`
`=1-5`
`=-4`
`i)(\sqrt{11}+11)/(11-\sqrt{11})+(11-\sqrt{11})/(11+\sqrt{11})`
`=(\sqrt{11}(\sqrt{11}+1))/(\sqrt{11}(\sqrt{11}-1))+(\sqrt{11}(\sqrt{11}-1))/(\sqrt{11}(\sqrt{11}+1))`
`=(\sqrt{11}+1)/(\sqrt{11}-1)+(\sqrt{11}-1)/(\sqrt{11}+1)`
`=((\sqrt{11}+1)^2+(\sqrt{11}-1)^2)/((\sqrt{11}+1)(\sqrt{11}-1))`
`=(11+2\sqrt{11}+1+11-2\sqrt{11}+1)/(11-1)`
`=24/10`
`=2,4`
`j)(\sqrt{10}+2\sqrt{7})/(\sqrt{14}+\sqrt{5})-1/(2-\sqrt{3})`
`=((\sqrt{10}+2\sqrt{7})(\sqrt{14}-\sqrt{5}))/((\sqrt{14}+\sqrt{5})(\sqrt{14}-\sqrt{5}))-(2+\sqrt{3})/((2-\sqrt{3})(2+\sqrt{3}))`
`=(2\sqrt{35}-5\sqrt{2}+14\sqrt{2}-2\sqrt{35})/(14-5)-(2+\sqrt{3})/(4-3)`
`=(9\sqrt{2})/9-(2+\sqrt{3})`
`=\sqrt{2}-2-\sqrt{3}`
