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a) 2/7+-3/8+11/7+1/3+1/7+5/-8
=(2/7+11/7+1/7)+(3/8+-5/8)+1/3
=2+2+1/3
=4+1/3
=13/3
b) -3/8+12/25+5/-8+2/-5+13/25
=(-3/8+-5/8)+(12/25+13/25)+-2/5
=-1+1+-2/5
=0+-2/5
=-2/5
c)7/8+1/8*3/8+1/8*5/8
=7/8+1/8*(3/8+5/8)
=7/8+1/8*1
=7/8+1/8
=1
a) 2/7+-3/8+11/7+1/3+1/7+5/-8
=(2/7+11/7+1/7)+(3/8+-5/8)+1/3
=2+2+1/3
=4+1/3
=13/3
b) -3/8+12/25+5/-8+2/-5+13/25
=(-3/8+-5/8)+(12/25+13/25)+-2/5
=-1+1+-2/5
=0+-2/5
=-2/5
c)7/8+1/8*3/8+1/8*5/8
=7/8+1/8*(3/8+5/8)
=7/8+1/8*1
=7/8+1/8
=1
\(=\frac{21.273.1333.4161.10101}{91.651.2451.6643.14763}\)
\(=\frac{3.7.13.21.31.43.73.57.91.111}{7.13.21.31.43.57.73.91.111.133}=\frac{3}{133}\)
Tuy nhiên cách làm trên phải có máy tính mới làm đc:
Có thể sử dụng công thức:
\(x^4+x^2+1=\left(x^2+x+1\right)\left(x^2-x+1\right)\)
Sau đó phân h:
\(2^4+2^2+1=\left(2^2+2+1\right)\left(2^2-2+1\right)=7.3\)
\(4^4+4^2+1=\left(4^2+4+1\right)\left(4^2-4+1\right)=21.13\)
....Tiếp tực làm thì sẽ ra đc kết quả:
\(=\frac{3.7.13.21.31.43.73.57.91.111}{7.13.21.31.43.57.73.91.111.133}=\frac{3}{133}\)
\(1)A=\frac{\frac{2}{5}+\frac{2}{7}-\frac{2}{9}-\frac{2}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{9}-\frac{4}{11}}\)
\(=\frac{2\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{9}-\frac{1}{11}\right)}{4\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{9}-\frac{1}{11}\right)}\)
\(=\frac{2}{4}=\frac{1}{2}\)
\(2)B=\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}.\frac{4^2}{4.5}\)
\(=\frac{1.1}{1.2}.\frac{2.2}{2.3}.\frac{3.3}{3.4}.\frac{4.4}{4.5}\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}\)
\(=\frac{1.2.3.4}{2.3.4.5}=\frac{1}{5}\)
\(3)C=\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}.\frac{5^2}{4.6}\)
\(=\frac{2.2.3.3.4.4.5.5}{1.3.2.4.3.5.4.6}\)
\(=\frac{2.5}{1.6}=\frac{2.5}{1.3.2}=\frac{5}{3}\)
\(4)D=\left(\frac{150}{1111}+\frac{5}{75}-\frac{14}{77}\right)\left(\frac{1}{5}-\frac{1}{6}-\frac{1}{30}\right)\)
\(=\left(\frac{150}{1111}+\frac{5}{75}-\frac{14}{77}\right)\left(\frac{6}{30}-\frac{5}{30}-\frac{1}{30}\right)\)
\(=\left(\frac{150}{1111}+\frac{5}{75}-\frac{14}{77}\right).0=0\)
\(5)M=8\frac{2}{7}-\left(3\frac{4}{9}+3\frac{9}{7}\right)\) \(N=\left(10\frac{2}{9}+2\frac{3}{5}\right)-6\frac{2}{9}\)
\(=\frac{58}{7}-\left(\frac{31}{9}+\frac{30}{7}\right)\) \(=\left(\frac{92}{9}+\frac{13}{5}\right)-\frac{56}{9}\)
\(=\frac{58}{7}-\left(\frac{217}{63}+\frac{270}{63}\right)\) \(=\left(\frac{460}{45}+\frac{117}{45}\right)-\frac{280}{45}\)
\(=\frac{58}{7}-\frac{487}{63}\) \(=\frac{577}{45}-\frac{280}{45}\)
\(=\frac{522}{63}-\frac{487}{63}=\frac{5}{9}\) \(=\frac{33}{5}\)
\(P=M-N\)
\(\Rightarrow P=\frac{5}{9}-\frac{33}{5}\)
\(\Rightarrow P=\frac{25}{45}-\frac{297}{45}\)
\(\Rightarrow P=\frac{-272}{45}\)
Vậy P = \(\frac{-272}{45}\)
\(6)E=10101\left(\frac{5}{111111}+\frac{5}{222222}-\frac{4}{3.7.11.13.37}\right)\)
\(=\frac{5}{11}+\frac{5}{22}-\left(10101.\frac{4}{111111}\right)\)
\(=\frac{10}{22}+\frac{5}{22}-\frac{4}{11}\)
\(=\frac{15}{22}-\frac{8}{22}=\frac{7}{22}\)
\(7)F=\frac{\frac{1}{3}+\frac{1}{7}-\frac{1}{13}}{\frac{2}{3}+\frac{2}{7}-\frac{2}{13}}.\frac{\frac{3}{4}-\frac{3}{16}-\frac{3}{256}+\frac{3}{64}}{1-\frac{1}{4}+\frac{1}{16}-\frac{1}{64}}+\frac{5}{8}\)
\(=\frac{1\left(\frac{1}{3}+\frac{1}{7}-\frac{1}{13}\right)}{2\left(\frac{1}{3}+\frac{1}{7}-\frac{1}{13}\right)}.\frac{3\left(\frac{1}{4}-\frac{1}{16}-\frac{1}{256}+\frac{1}{64}\right)}{1\left(1-\frac{1}{4}+\frac{1}{16}-\frac{1}{64}\right)}+\frac{5}{8}\)
\(=\frac{1}{2}.\frac{3\left(\frac{16}{64}-\frac{4}{64}+\frac{1}{64}-\frac{1}{256}\right)}{1\left(\frac{64}{64}-\frac{16}{64}+\frac{4}{64}-\frac{1}{64}\right)}+\frac{5}{8}\)
\(=\frac{1}{2}.\frac{3\left(\frac{13}{64}-\frac{1}{256}\right)}{1.\frac{51}{64}}+\frac{5}{8}\)
\(=\frac{1}{2}.\frac{3\left(\frac{52}{256}-\frac{1}{256}\right)}{\frac{51}{64}}+\frac{5}{8}\)
\(=\frac{1}{2}.\frac{3\left(\frac{51}{256}\right)}{\frac{51}{64}}+\frac{5}{8}\)
\(=\frac{1}{2}.\frac{\frac{153}{256}}{\frac{51}{64}}+\frac{5}{8}\)
\(=\frac{1}{2}.\frac{153}{256}:\frac{51}{64}+\frac{5}{8}\)
\(=\frac{1}{2}.\frac{3}{4}+\frac{5}{8}\)
\(=\frac{3}{8}+\frac{5}{8}=1\)
Xin lỗi tớ đã làm hết buổi tối mà chỉ có 7 bài mong bạn thông cảm cho mình nhé !
a) \(A=\left(-1\right).\left(-1\right)^2.\left(-1\right)^3.\left(-1\right)^4.....\left(-1\right)^{2016}.\left(-1\right)^{2017}\)
\(=\left[\left(-1\right).\left(-1\right)^3.\left(-1\right)^5.....\left(-1\right)^{2017}\right].\left[\left(-1\right)^2.\left(-1\right)^4.....\left(-1\right)^{2016}\right]\)
TỪ 1 ĐẾN 2017 CÓ 1009 SỐ LẺ NÊN
\(\left(-1\right).\left(-1\right)^3....\left(-1\right)^{2017}=\left(-1\right)\)
TÍCH CỦA \(\left(-1\right)^2.\left(-1\right)^4....\left(-1\right)^{2016}\)LÀ TÍCH CỦA CÁC LŨY THỪA MŨ CHẴN NÊN \(=1\)
\(A=\left(-1\right).1=-1\)
b) \(\frac{1}{7.7^4.11^2.77^4}.\frac{1}{7^2}.7^8.\left(-11\right)^3.7^{15}.11^{18}\)
\(=\frac{7^8.\left(-11\right)^3.7^{15}.11^{18}}{7.7^4.11^2.7^4.11^4.7^2}\)
\(=\frac{7^{23}.\left(-11\right)^{21}}{7^{11}.11^6}\)
\(=7^{12}.\left(-11\right)^{15}\)
Ta thấy từ 1 đến 2016 là có 2016 số chia thành 1008 là số chẵn nên tích 2016 số đầu là 1 số cuối là -1 nên tích cần tìm là -1