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Q= (2 căn x -9)/(x-5 căn x +6)-(căn x + 3)/(căn x -2)-(2 căn x+1)/3 căn x)
tìm x để Q<1
[laTEX]txd: x > 0 \\ \\ Q = \frac{2.\sqrt{x}-9}{(\sqrt{x}-3)(\sqrt{x}-2)} - \frac{\sqrt{x}+3}{\sqrt{x}-2} - \frac{2.\sqrt{x}+1}{3.\sqrt{x}} \\ \\ \\ Q = \frac{(2.\sqrt{x}-9).3\sqrt{x} - 3\sqrt{x}.(x-9) - (2.\sqrt{x}+1)(x - 5.\sqrt{x}+6)}{3\sqrt{x}.(\sqrt{x}-3)(\sqrt{x}-2)} \\ \\ \\ Q = \frac{-5.x.\sqrt{x}+ 15x - 7.\sqrt{x}- 6}{3\sqrt{x}.(\sqrt{x}-3)(\sqrt{x}-2)} \\ \\ \\Q = \frac{(\sqrt{x}-2)( -5x + 5.\sqrt{x}+3)}{3\sqrt{x}.(\sqrt{x}-3)(\sqrt{x}-2)} \\ \\ \\ Q = \frac{-5x + 5.\sqrt{x}+3}{3\sqrt{x}.(\sqrt{x}-3) } [/laTEX]
tìm x để Q < 1 ta lấy Q - 1 < 0
[laTEX]\frac{-5x + 5.\sqrt{x}+3}{3\sqrt{x}.(\sqrt{x}-3) } - 1 < 0 \Leftrightarrow \frac{-8x+14\sqrt{x}+3}{3\sqrt{x}.(\sqrt{x}-3) } < 0 [/laTEX]
đến đây lập bảng xét dấu
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