Question

Tính giá trị một cách hợp lý

A = 4,8 . ( 3,1 - 1,5 ) + 1.5 . ( 4,8 - 3,1 )

B = \(\dfrac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)

C = -1 -\(\dfrac{1}{3}-\dfrac{1}{6}-\dfrac{1}{10}-\dfrac{1}{15}-\dfrac{1}{21}-\dfrac{1}{28}-\dfrac{1}{36}-\dfrac{1}{45}\)

Answer 1

\(A=4,8.\left(3,1-1,5\right)+1,5.\left(4,8-3,1\right)\)

\(A=4,8.3,1-4,8.1,5+1,5.4,8-1,5.3,1\)

\(A=3,1.\left(4,8-1,5\right)-4,8\left(1,5+1,5\right)\)

\(A=3,1.3,3-4,8.3\)

\(A=10,23-14,4=-4,17\)

Answer 2

\(B=\dfrac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}=\dfrac{2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4}{\left(2.3\right)^9.2^{10}+\left(3.2^2\right)^{10}}=\dfrac{2^{19}.3^9+3.5.2^{18}.3^8}{2.3^9.2^{10}+3^{10}.\left(2^2\right)^{10}}=\dfrac{2^{19}.3^9+3^9.2^{18}.5}{2^{11}.3^9+3^{10}.2^{20}}=\dfrac{2^{18}.3^9\left(2+5\right)}{2^{11}.3^9\left(1+3.2^9\right)}=\dfrac{2^7.7}{1+3.2^9}\)

Answer 3

\(C=-1-\dfrac{1}{3}-\dfrac{1}{6}-\dfrac{1}{10}-\dfrac{1}{15}-\dfrac{1}{21}-\dfrac{1}{28}-\dfrac{1}{36}-\dfrac{1}{45}\)

\(\Rightarrow C=\dfrac{-1}{2}\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\right)\)

\(\Rightarrow C=\dfrac{-1}{2}\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{9.10}\right)\)

\(\Rightarrow C=\dfrac{-1}{2}\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\)

\(\Rightarrow C=\dfrac{-1}{2}\left(1-\dfrac{1}{10}\right)\)

\(\Rightarrow C=\dfrac{-1}{2}.\dfrac{9}{10}\)

\(\Rightarrow C=\dfrac{-9}{20}\)