C= {[(căn x -2) phần (x-1)] – [(căn x +2) phần (x – 2 căn x +1)]}* (1-x) ^2 phần 2

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C= {[(căn x -2) phần (x-1)] – [(căn x +2) phần (x – 2 căn x +1)]}* (1-x) ^2 phần 2

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Samantha 3 tháng 2021-09-26T07:51:03+00:00 1 Answers 7 views 0

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    2021-09-26T07:52:56+00:00

    \[\begin{array}{l}
    C = \left( {\frac{{\sqrt x – 2}}{{x – 1}} – \frac{{\sqrt x + 2}}{{x – 2\sqrt x + 1}}} \right).\frac{{{{\left( {1 – x} \right)}^2}}}{2}\\
    DK:\,\,\,x \ge 0,\,\,\,x \ne 1\\
    \Rightarrow C = \left[ {\frac{{\sqrt x – 2}}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}} – \frac{{\sqrt x + 2}}{{{{\left( {\sqrt x – 1} \right)}^2}}}} \right].\frac{{{{\left( {x – 1} \right)}^2}}}{2}\\
    = \frac{{\left( {\sqrt x – 2} \right)\left( {\sqrt x – 1} \right) – \left( {\sqrt x + 2} \right)\left( {\sqrt x + 1} \right)}}{{\left( {\sqrt x – 1} \right)\left( {x – 1} \right)}}.\frac{{{{\left( {x – 1} \right)}^2}}}{2}\\
    = \frac{{x – 3\sqrt x + 2 – x – 3\sqrt x – 2}}{{\left( {\sqrt x – 1} \right)\left( {x – 1} \right)}}.\frac{{{{\left( {x – 1} \right)}^2}}}{2}\\
    = \frac{{ – 6\sqrt x }}{{\sqrt x – 1}}.\frac{{x – 1}}{2} = \frac{{ – 3\sqrt x \left( {x – 1} \right)}}{{\sqrt x – 1}}\\
    = \frac{{ – 3\sqrt x \left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}}{{\sqrt x – 1}} = – 3\sqrt x \left( {\sqrt x + 1} \right).
    \end{array}\]

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