Đáp án:
Giải thích các bước giải:
Bài 3
`a)`
Đk: ` x ne 4; x ne 0`
`M = \sqrt{x}/(\sqrt{x}-2)-2/(\sqrt{x}+2)-(4\sqrt{x})/(x-4)`
`M = (\sqrt{x}(\sqrt{x}+2))/(x-4)-(2(\sqrt{x}-2))/(x-4)-(4\sqrt{x})/(x-4)`
`M = (x+2\sqrt{x}-2\sqrt{x}+4-4\sqrt{x})/(x-4)`
`M = (x+4-4\sqrt{x})/(x-4)`
`M = (\sqrt{x} - 2)^2/((\sqrt{x} - 2)(\sqrt{x} + 2))`
`M = (\sqrt{x} - 2)/(\sqrt{x} + 2)`
`b)`
`M = 1/5`
`=> (\sqrt{x} - 2)/(\sqrt{x} + 2) = 1/5 `
`=> 5(\sqrt{x} - 2) = \sqrt{x} + 2`
`=> 5\sqrt{x} - 10 = \sqrt{x} + 2`
`=> 4\sqrt{x} = 12`
`=> \sqrt{x} = 3`
`=> x = 9`
`c)`
`M < 1/2`
`=> (\sqrt{x} - 2)/(\sqrt{x} + 2) < 1/2 `
`=> 2(\sqrt{x} - 2) < \sqrt{x} + 2`
`=> 2\sqrt{x} - 4 < \sqrt{x} + 2`
`=> \sqrt{x} < 6`
`=> x<36`
Bài 4
`M = \sqrt{2-\sqrt{3}} - \sqrt{2-\sqrt{3}}`
`M = (2\sqrt{2+\sqrt{3}})/2 - (2\sqrt{2-\sqrt{3}})/2`
`M = (\sqrt{8+4\sqrt{3}})/2 - (\sqrt{8-4\sqrt{3}})/2`
`M = (\sqrt{2+4\sqrt{3}+6})/2 - (\sqrt{2-4\sqrt{3}+6})/2`
`M = (\sqrt{(\sqrt{6}+\sqrt{2})^2})/2 - (\sqrt{(\sqrt{6}-\sqrt{2})^2})/2`
`M = (\sqrt{6}+\sqrt{2})/2 - (\sqrt{6}-\sqrt{2})/2`
`M = (2\sqrt{2})/2`
`M = \sqrt{2}`
