Đáp án:
$a)
A=-10000\\
b)
B=-4900\\
c)
C=\dfrac{114}{833}\\
d)
D=\dfrac{81}{10}$
Giải thích các bước giải:
$a)
A=35.73-135.27+35.27-73.135\\
=35(73+27)-135(27+73)\\
=35.100-135.100\\
=3500-13500=-10000\\
b)
B=96.7^2-37.7^2+15.7^2-49.174\\
=96.7^2-37.7^2+15.7^2-7^2.174\\
=7^2(96-37+15-174)\\
=7^2(-100)\\
=-4900\\
c)
C=\dfrac{2}{7}.\left ( \dfrac{22}{19}-\dfrac{12}{51} \right )+\dfrac{2}{7}.\left ( \dfrac{-3}{19}+\dfrac{-2}{7}\right )\\
=\dfrac{2}{7}.\left ( \dfrac{22}{19}-\dfrac{12}{51}+\dfrac{-3}{19}+\dfrac{-2}{7} \right )\\
=\dfrac{2}{7}.\left ( \dfrac{22}{19}+\dfrac{-3}{19}+\dfrac{-2}{7}-\dfrac{12}{51} \right )\\
=\dfrac{2}{7}.\left ( \dfrac{19}{19}+\dfrac{-2}{7}-\dfrac{12}{51} \right )\\
=\dfrac{2}{7}.\left ( 1+\dfrac{-2}{7}-\dfrac{12}{51} \right )\\
=\dfrac{2}{7}.\left ( \dfrac{357}{357}+\dfrac{-102}{357}-\dfrac{84}{357} \right )\\
=\dfrac{2}{7}.\dfrac{171}{357}\\
=\dfrac{114}{833}\\
d)
D=\dfrac{1}{2}+\dfrac{5}{6}+\dfrac{11}{12}+\dfrac{19}{20}+\dfrac{29}{30}+\dfrac{41}{42}+\dfrac{55}{56}+\dfrac{71}{72}+\dfrac{89}{90}\\
=1-\dfrac{1}{2}+1-\dfrac{1}{6}+1-\dfrac{1}{12}+1-\dfrac{1}{20}+1-\dfrac{1}{30}+1-\dfrac{1}{42}+1-\dfrac{1}{56}+1-\dfrac{1}{72}+1-\dfrac{1}{90}\\
=(1+1+...+1)-\left (\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90} \right )\\
=9-\left ( \dfrac{1}{2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10} \right )\\
=9-\left ( \dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10} \right )\\
=9-\left ( 1-\dfrac{1}{10} \right )\\
=9-1+\dfrac{1}{10}\\
=8+\dfrac{1}{10}\\
=\dfrac{80}{10}+\dfrac{1}{10}\\
=\dfrac{81}{10}$
