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a/ \(3a=2b;4b=3c\)
=> \(6a=4b=3c\)
=> \(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}=\dfrac{4b}{12}=\dfrac{5c}{20}=\dfrac{a+4b-5c}{2+12-20}=\dfrac{-30}{-6}=5\)
=> \(\left\{{}\begin{matrix}a=10\\b=15\\c=20\end{matrix}\right.\)
=> B
Đặt \(\frac{a}{12}=\frac{b}{9}=\frac{c}{5}=k\Leftrightarrow a=12k;b=9k;c=5k\)
Do abc = 20
\(\Rightarrow12k.9k.5k=20\)
\(\Rightarrow540k^3=20\)
\(\Rightarrow k^3=\frac{1}{27}\Leftrightarrow k=\frac{1}{3}\)
\(\Rightarrow a=\frac{1}{3}.12=4;b=\frac{1}{3}.9=3;c=\frac{1}{3}.5=\frac{5}{3}\)
a, - 1,2 + (- 0,8) + 0,25 + 5,75 - 2021
= - (1,2 + 0,8) + (0,25 + 5,75) - 2021
= - 2 + 6 - 2021
= 4 - 2021
= - 2017
b, - 0,1 + \(\dfrac{16}{9}\) + 11,1 - \(\dfrac{20}{9}\)
= (11,1 - 0,1) - (\(\dfrac{20}{9}\) - \(\dfrac{16}{9}\))
= 11 - \(\dfrac{4}{9}\)
= \(\dfrac{95}{5}\)
Đề bài sai chỗ ... - 99 nhé, nếu là .99 sẽ hợp lí hơn =))
\(A=\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^{10}.6^{19}-7.2^{29}.27^6}=\frac{5.\left(2^2\right)^{15}\left(3^2\right)^9-2^2.3^{20}.\left(2^3\right)^9}{5.2^{10}.\left(2.3\right)^{19}-7.2^2.\left(3^2\right)^6}\)
\(A=\frac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^{10}.2^{19}.3^{19}-7.2^{29}.3^{18}}\)
\(A=\frac{5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{29}.3^{19}-7.2^{29}.3^{18}}\)
\(A=\frac{2^{29}.3^{18}.\left(5.2-3^2\right)}{2^{29}.3^{18}.\left(5.3-7\right)}\)
\(A=\frac{10-9}{15-7}=\frac{1}{8}\)
a: \(A=\dfrac{3^3\cdot2^3+3^3\cdot2^2+3^3\cdot1}{-13}=\dfrac{27\left(2^3+2^2+1\right)}{-13}=-27\)
b: \(B=\dfrac{2\cdot2^{12}\cdot3^6+2^{11}\cdot3^9}{2^3\cdot2^7\cdot3^7+2^7\cdot2^3\cdot5\cdot3^8}\)
\(=\dfrac{2^{13}\cdot3^6+2^{11}\cdot3^9}{2^{10}\cdot3^7+2^{10}\cdot5\cdot3^8}\)
\(=\dfrac{2^{11}\cdot3^6\left(2^2+3^3\right)}{2^{10}\cdot3^7\left(1+5\cdot3\right)}=\dfrac{2}{3}\cdot\dfrac{4+27}{1+15}=\dfrac{2}{3}\cdot\dfrac{31}{16}=\dfrac{31}{24}\)
c: \(C=\dfrac{5\cdot2^{30}\cdot3^{18}-2^{29}\cdot3^{20}}{5\cdot2^{35}\cdot3^{19}-7\cdot2^{29}\cdot3^{18}}\)
\(=\dfrac{2^{29}\cdot3^{18}\left(5\cdot2-3^2\right)}{2^{29}\cdot3^{18}\left(5\cdot2^6-7\right)}=\dfrac{10-9}{5\cdot64-7}=\dfrac{1}{313}\)
Áp dụng tính chất của dãy tỉ số bằng nhau ta có a/9=b/11 suy ra a+b/9+11=20/20=1 suy ra a=1.9=9 b=1.11=11 cho xin