Toán Lớp 9: Tính: B= căn( 1 + 2017² + 2017²/2018² + 2017/2018
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Toán Lớp 9: Tính: B= căn( 1 + 2017² + 2017²/2018² + 2017/2018
ai giúp em bài này cấy ạ
Comments ( 1 )
B = \sqrt {1 + {{2017}^2} + \dfrac{{{{2017}^2}}}{{{{2018}^2}}}} + \dfrac{{2017}}{{2018}}\\
= \sqrt {\left( {1 + 2.2017 + {{2017}^2}} \right) – 2.2017 + {{\left( {\dfrac{{2017}}{{2018}}} \right)}^2}} + \dfrac{{2017}}{{2018}}\\
= \sqrt {\left( {{{2017}^2} + 2.2017.1 + {1^2}} \right) – 2.2017 + {{\left( {\dfrac{{2017}}{{2018}}} \right)}^2}} + \dfrac{{2017}}{{2018}}\\
= \sqrt {{{\left( {2017 + 1} \right)}^2} – 2.2017 + {{\left( {\dfrac{{2017}}{{2018}}} \right)}^2}} + \dfrac{{2017}}{{2018}}\\
= \sqrt {{{2018}^2} – 2.2018.\dfrac{{2017}}{{2018}} + \left( {{{\dfrac{{2017}}{{2018}}}^2}} \right)} + \dfrac{{2017}}{{2018}}\\
= \sqrt {{{\left( {2018 – \dfrac{{2017}}{{2018}}} \right)}^2}} + \dfrac{{2017}}{{2018}}\\
= \left| {2018 – \dfrac{{2017}}{{2018}}} \right| + \dfrac{{2017}}{{2018}}\\
= \left( {2018 – \dfrac{{2017}}{{2018}}} \right) + \dfrac{{2017}}{{2018}}\\
= 2018
\end{array}\)