Toán Lớp 9: cho 1
Toán Lớp 9: cho 1
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Toán Lớp 9: cho 1
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Dk:1 < x < 2\\
\Leftrightarrow x – 1 < 1\\
\Leftrightarrow \sqrt {x – 1} < 1\\
A = \left[ {\sqrt {\left( {x – \sqrt {4\left( {x – 1} \right)} } \right)} + \sqrt {x + \sqrt {4\left( {x – 1} \right)} } } \right].\left( {1 – \dfrac{1}{{x – 1}}} \right)\\
= \left( {\sqrt {x – 2\sqrt {x – 1} } + \sqrt {x + 2\sqrt {x – 1} } } \right).\dfrac{{x – 1 – 1}}{{x – 1}}\\
= \left[ {\sqrt {x – 1 – 2\sqrt {x – 1} + 1} + \sqrt {x – 1 + 2\sqrt {x – 1} + 1} } \right].\dfrac{{x – 2}}{{x – 1}}\\
= \left( {\sqrt {{{\left( {\sqrt {x – 1} – 1} \right)}^2}} + \sqrt {{{\left( {\sqrt {x – 1} + 1} \right)}^2}} } \right).\dfrac{{x – 2}}{{x – 1}}\\
= \left( {1 – \sqrt {x – 1} + \sqrt {x – 1} + 1} \right).\dfrac{{x – 2}}{{x – 1}}\\
= 2.\dfrac{{x – 2}}{{x – 1}}\\
= \dfrac{{2x – 4}}{{x – 1}}
\end{array}$