Toán C= {[(căn x -2) phần (x-1)] – [(căn x +2) phần (x – 2 căn x +1)]}* (1-x) ^2 phần 2 26/09/2021 By Samantha C= {[(căn x -2) phần (x-1)] – [(căn x +2) phần (x – 2 căn x +1)]}* (1-x) ^2 phần 2
\[\begin{array}{l} C = \left( {\frac{{\sqrt x – 2}}{{x – 1}} – \frac{{\sqrt x + 2}}{{x – 2\sqrt x + 1}}} \right).\frac{{{{\left( {1 – x} \right)}^2}}}{2}\\ DK:\,\,\,x \ge 0,\,\,\,x \ne 1\\ \Rightarrow C = \left[ {\frac{{\sqrt x – 2}}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}} – \frac{{\sqrt x + 2}}{{{{\left( {\sqrt x – 1} \right)}^2}}}} \right].\frac{{{{\left( {x – 1} \right)}^2}}}{2}\\ = \frac{{\left( {\sqrt x – 2} \right)\left( {\sqrt x – 1} \right) – \left( {\sqrt x + 2} \right)\left( {\sqrt x + 1} \right)}}{{\left( {\sqrt x – 1} \right)\left( {x – 1} \right)}}.\frac{{{{\left( {x – 1} \right)}^2}}}{2}\\ = \frac{{x – 3\sqrt x + 2 – x – 3\sqrt x – 2}}{{\left( {\sqrt x – 1} \right)\left( {x – 1} \right)}}.\frac{{{{\left( {x – 1} \right)}^2}}}{2}\\ = \frac{{ – 6\sqrt x }}{{\sqrt x – 1}}.\frac{{x – 1}}{2} = \frac{{ – 3\sqrt x \left( {x – 1} \right)}}{{\sqrt x – 1}}\\ = \frac{{ – 3\sqrt x \left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}}{{\sqrt x – 1}} = – 3\sqrt x \left( {\sqrt x + 1} \right). \end{array}\] Trả lời
\[\begin{array}{l}
C = \left( {\frac{{\sqrt x – 2}}{{x – 1}} – \frac{{\sqrt x + 2}}{{x – 2\sqrt x + 1}}} \right).\frac{{{{\left( {1 – x} \right)}^2}}}{2}\\
DK:\,\,\,x \ge 0,\,\,\,x \ne 1\\
\Rightarrow C = \left[ {\frac{{\sqrt x – 2}}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}} – \frac{{\sqrt x + 2}}{{{{\left( {\sqrt x – 1} \right)}^2}}}} \right].\frac{{{{\left( {x – 1} \right)}^2}}}{2}\\
= \frac{{\left( {\sqrt x – 2} \right)\left( {\sqrt x – 1} \right) – \left( {\sqrt x + 2} \right)\left( {\sqrt x + 1} \right)}}{{\left( {\sqrt x – 1} \right)\left( {x – 1} \right)}}.\frac{{{{\left( {x – 1} \right)}^2}}}{2}\\
= \frac{{x – 3\sqrt x + 2 – x – 3\sqrt x – 2}}{{\left( {\sqrt x – 1} \right)\left( {x – 1} \right)}}.\frac{{{{\left( {x – 1} \right)}^2}}}{2}\\
= \frac{{ – 6\sqrt x }}{{\sqrt x – 1}}.\frac{{x – 1}}{2} = \frac{{ – 3\sqrt x \left( {x – 1} \right)}}{{\sqrt x – 1}}\\
= \frac{{ – 3\sqrt x \left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}}{{\sqrt x – 1}} = – 3\sqrt x \left( {\sqrt x + 1} \right).
\end{array}\]