Tính giá trị biểu thức (A49^12+A49^11)/A49^10-(A17^10+A17^9)/A17^8 05/09/2021 Bởi Reese Tính giá trị biểu thức (A49^12+A49^11)/A49^10-(A17^10+A17^9)/A17^8
Đáp án: $1440$ Giải thích các bước giải: \[\begin{array}{l}\dfrac{{A_{49}^{12} + A_{49}^{11}}}{{A_{49}^{10}}} – \dfrac{{A_{17}^{10} + A_{17}^9}}{{A_{17}^8}}\\ = \dfrac{{\dfrac{{49!}}{{\left( {49 – 12} \right)!}} + \dfrac{{49!}}{{\left( {49 – 11} \right)!}}}}{{\dfrac{{49!}}{{\left( {49 – 10} \right)!}}}} – \dfrac{{\dfrac{{17!}}{{\left( {17 – 10} \right)!}} + \dfrac{{17!}}{{\left( {17 – 9} \right)!}}}}{{\dfrac{{17!}}{{\left( {17 – 8} \right)!}}}}\\ = \dfrac{{\dfrac{{49!}}{{37!}} + \dfrac{{49!}}{{38!}}}}{{\dfrac{{49!}}{{39!}}}} – \dfrac{{\dfrac{{17!}}{{7!}} + \dfrac{{17!}}{{8!}}}}{{\dfrac{{17!}}{{9!}}}} = \dfrac{{\dfrac{{49!}}{{37!}}\left( {1 + \dfrac{1}{{38}}} \right)}}{{\dfrac{1}{{39.38}}.\dfrac{{49!}}{{37!}}}} – \dfrac{{\dfrac{{17!}}{{7!}}\left( {1 + \dfrac{1}{8}} \right)}}{{\dfrac{1}{{9.8}}.\dfrac{{17!}}{{7!}}}}\\ = \dfrac{{39}}{{38}}.\dfrac{{39.38}}{1} – \dfrac{9}{8}.\dfrac{{8.9}}{1} = 39.39 – 9.9 = 1440\end{array}\] Bình luận
Đáp án:
$1440$
Giải thích các bước giải:
\[\begin{array}{l}
\dfrac{{A_{49}^{12} + A_{49}^{11}}}{{A_{49}^{10}}} – \dfrac{{A_{17}^{10} + A_{17}^9}}{{A_{17}^8}}\\
= \dfrac{{\dfrac{{49!}}{{\left( {49 – 12} \right)!}} + \dfrac{{49!}}{{\left( {49 – 11} \right)!}}}}{{\dfrac{{49!}}{{\left( {49 – 10} \right)!}}}} – \dfrac{{\dfrac{{17!}}{{\left( {17 – 10} \right)!}} + \dfrac{{17!}}{{\left( {17 – 9} \right)!}}}}{{\dfrac{{17!}}{{\left( {17 – 8} \right)!}}}}\\
= \dfrac{{\dfrac{{49!}}{{37!}} + \dfrac{{49!}}{{38!}}}}{{\dfrac{{49!}}{{39!}}}} – \dfrac{{\dfrac{{17!}}{{7!}} + \dfrac{{17!}}{{8!}}}}{{\dfrac{{17!}}{{9!}}}} = \dfrac{{\dfrac{{49!}}{{37!}}\left( {1 + \dfrac{1}{{38}}} \right)}}{{\dfrac{1}{{39.38}}.\dfrac{{49!}}{{37!}}}} – \dfrac{{\dfrac{{17!}}{{7!}}\left( {1 + \dfrac{1}{8}} \right)}}{{\dfrac{1}{{9.8}}.\dfrac{{17!}}{{7!}}}}\\
= \dfrac{{39}}{{38}}.\dfrac{{39.38}}{1} – \dfrac{9}{8}.\dfrac{{8.9}}{1} = 39.39 – 9.9 = 1440
\end{array}\]