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gọi x là số cần tìm
X:21=10(dư14)
X= 10.21+14
X= 210+14
X= 224
Vậy số cần tìm là: 224
\(\dfrac{1}{2}+\dfrac{5}{6}+\dfrac{11}{12}+\dfrac{19}{20}+\dfrac{29}{30}+\dfrac{41}{42}+\dfrac{55}{56}+\dfrac{71}{72}\)\(+\dfrac{89}{90}\)
=\(\left(1-\dfrac{1}{2}\right)+\left(1-\dfrac{1}{6}\right)+\left(1-\dfrac{1}{12}\right)+\left(1-\dfrac{1}{20}\right)\)\(+\)\(\left(1-\dfrac{1}{30}\right)+\left(1-\dfrac{1}{42}\right)+\left(1-\dfrac{1}{56}\right)+\)\(\left(1-\dfrac{1}{72}\right)+\left(1-\dfrac{1}{90}\right)\)
=(1+1+1+1+1+1+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-\(\left(\dfrac{1}{1x2}+\dfrac{1}{2x3}+\dfrac{1}{3x4}+\dfrac{1}{4x5}+\dfrac{1}{5x6}+\dfrac{1}{6x7}+\dfrac{1}{7x8}+\dfrac{1}{8x9}+\dfrac{1}{9x10}\right)\)
=9-\(\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\right)\)
=9-\(\left(\dfrac{1}{1}-\dfrac{1}{10}\right)\)
=9-\(\dfrac{9}{10}\)
=\(\dfrac{81}{10}\)
=> (x-11):3 - 273=91 => (x-11):3=364 => x-11=1092 => x=1103
(x-11):3-21.13=91
(x-11):3-273=91
(x-11):(-270)=91
(x-11) =91.(-270)
(x-11) =(-24570)
x =(-24570)+11
x =-24550