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13 tháng 10 2017
\(a,\dfrac{121.75.130.169}{39.60.11.198}=\dfrac{11.11.25.3.13.10.169}{13.3.6.10.11.11.18}=\dfrac{25.169}{6.18}\)
1 tháng 2 2019
a) =\(\left[\left(12+1\right)^2+\left(12+2\right)^2\right]:\left(13^2+14^2\right)\)
=1
b)=(1.2.3....8).(9-1-8)
=(1.2.3....8).0
=0
mik chỉ giải được zậy thôi.
t mik nha.
10 tháng 3 2020
a) Đặt \(A=\left(10^2+11^2+12^2\right)\div\left(13^2+14^2\right)\)
- Ta có: \(A=\left(100+121+144\right)\div\left(169+196\right)\)
\(\Leftrightarrow A=365\div365=1\)
Vậy \(A=1\)
b) Đặt \(B=1.2.3.....9-1.2.3.....8-1.2.3.....8^2\)
- Ta có: \(B=1.2.3.....8.\left(9-1\right)-1.2.3.....8^2\)
\(\Leftrightarrow B=1.2.3.....8.8-1.2.3.....8.8=0\)
Vậy \(B=0\)
c) Đặt \(C=\frac{\left(3.4.2^{16}\right)^2}{11.2^{13}.4^{11}-16^9}\)
- Ta có: \(C=\frac{3^2.4^2.2^{32}}{11.2^{13}.2^{22}-2^{36}}\)
\(\Leftrightarrow C=\frac{3^2.2^4.2^{32}}{11.2^{35}-2^{36}}\)
\(\Leftrightarrow C=\frac{3^2.2^{36}}{2^{35}.\left(11-2\right)}\)
\(\Leftrightarrow C=\frac{9.2^{36}}{2^{35}.9}\)
\(\Leftrightarrow C=2\)
Vậy \(C=2\)
d) Đặt \(D=1152-\left(374+1152\right)+\left(-65+374\right)\)
- Ta có: \(D=1152-374-1152-65+374\)
\(\Leftrightarrow D=\left(1152-1152\right)+\left(374-374\right)-65\)
\(\Leftrightarrow D=-65\)
Vậy \(D=-65\)
5 tháng 5 2018
\(\frac{8^2}{7.9}.\frac{9^2}{8.10}...\frac{14^2}{13.15}\)
\(\frac{8.8}{7.9}.\frac{9.9}{8.10}...\frac{14.14}{13.15}\)
\(\frac{8.9...14}{7.8...13}.\frac{8.9...14}{9.10...15}\)
\(\frac{14}{7}.\frac{8}{15}\)
\(2.\frac{8}{15}\)
\(\frac{16}{15}\)
5 tháng 5 2018
(8.9.10.11.12.13.14)(8.9.10.11.12.13.14)/7.8.9.10.11.12.13).(9.10.11.12.13.14.15)
=14.8/7.15
=16/15
k cho mình nhá
N
4
11 tháng 7 2016
\(\left(10^2+11^2+12^2\right):\left(13^2+14^2\right)\)
\(=\left(100+121+144\right):\left(169+196\right)\)
\(=\frac{365}{365}=1\)
11 tháng 7 2016
(102 + 112 + 122) : (132 + 142)
= (100 + 121 + 144) : (169 + 196)
= 365 : 365
= 1
Ủng hộ mk nha ^_-
4 tháng 4 2019
a,\(\frac{-2}{3}+\frac{1}{5}=\frac{-2.5}{3.5}+\frac{3.1}{3.5}=-\frac{10}{15}+\frac{3}{15}=-\frac{7}{15}\)
b,\(3\frac{11}{13}-5\frac{11}{3}=3+\frac{11}{13}-(5+\frac{11}{13})=\left(3-5\right)+\left(\frac{11}{13}-\frac{11}{13}\right)=-2+0=-2\)
c,\(1\frac{2}{3}:(-\frac{5}{3})=\frac{5}{3}:\left(-\frac{5}{3}\right)=\frac{5.3}{3.\left(-5\right)}=\frac{15}{-15}=-1\)
d,\(\frac{31}{17}+\frac{-5}{13}+\frac{-8}{13}-\frac{14}{17}=\left(\frac{31}{17}-\frac{14}{17}\right)+\left(\frac{-5}{13}+\frac{-8}{13}\right)=1+\left(-1\right)=0\)
Tìm x:
a,x+12=8
x=8-12
x=-4
b,\(\frac{2}{3}x+\frac{1}{2}=\frac{1}{10}\)
\(\frac{2}{3}x=\frac{1}{10}-\frac{1}{2}\)
\(\frac{2}{3}x=\frac{1}{10}-\frac{5}{10}\)
\(\frac{2}{3}x=\frac{2}{5}\)
\(x=\frac{2}{5}:\frac{2}{3}\)
\(x=\frac{6}{10}\)
\(x=\frac{3}{5}\)
4 tháng 4 2019
a) \(\frac{-2}{3}+\frac{1}{5}=\frac{-10}{15}+\frac{3}{15}=\frac{-10+3}{15}=\frac{-7}{15}\)
b) \(3\frac{11}{13}-5\frac{11}{13}=\frac{50}{13}-\frac{76}{13}=\frac{50-76}{13}=\frac{-26}{13}=-2\)
c) \(1\frac{2}{3}:\frac{-5}{3}=\frac{5}{3}:\frac{-5}{3}=\frac{5}{3}\times\frac{3}{-5}=\frac{15}{-15}=-1\)
d) \(\frac{31}{17}+\frac{-5}{13}+\frac{-8}{13}-\frac{14}{17}\)
\(=\left(\frac{31}{17}-\frac{14}{17}\right)+\left(\frac{-5}{13}+\frac{-8}{13}\right)\)
\(=\left(\frac{31-14}{17}\right)+\left(\frac{-5-8}{13}\right)\)
\(=\frac{17}{17}+\frac{-13}{13}\)
\(=1+\left(-1\right)\)
\(=0\)
TÌM x
a) \(x+12=8\)
\(\Leftrightarrow x=8-12\)
\(\Leftrightarrow x=-4\)
b) \(\frac{2}{3}x+\frac{1}{2}=\frac{1}{10}\)
\(\Leftrightarrow\frac{2}{3}x=\frac{1}{10}-\frac{1}{2}=\frac{1}{10}-\frac{5}{10}=\frac{1-5}{10}\)
\(\Leftrightarrow\frac{2}{3}x=\frac{-4}{10}=\frac{-2}{5}\)
\(\Leftrightarrow x=\frac{-2}{5}:\frac{2}{3}=\frac{-2}{5}\times\frac{3}{2}\)
\(\Leftrightarrow x=\frac{-6}{10}=\frac{-3}{5}\)
6 tháng 4 2017
a,(10^2+11^2+12^2):(13^2+14^2)
=(100+121+144);(169+196)
=365:365
=1
b,1.2.3...9-1.2.3...8-1.2.3...8^2=0
30 tháng 3 2017
a)=(100+121+144):(169+196)=365:365=1
b)=1.2.3...8.(9-1-8)=1.2.3...8.0=0
k mk nhaa
21 tháng 5 2017
d)
đặt A = 1 + 2 + 22 + ... + 280
2A = 2 + 22 + 23 + ... + 281
2A - A = ( 2 + 22 + 23 + ... + 281 ) - ( 1 + 2 + 22 + ... + 280 )
A = 281 - 1 > 281 - 2
e)
đặt \(A=\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+...+\frac{899}{900}\)
\(A=\left(1-\frac{1}{4}\right)+\left(1-\frac{1}{9}\right)+\left(1-\frac{1}{16}\right)+...+\left(1-\frac{1}{900}\right)\)
\(A=\left(1+1+1+...+1\right)-\left(\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+...+\frac{1}{900}\right)\)
\(A=29-\left(\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+...+\frac{1}{900}\right)\)
đặt \(B=\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+...+\frac{1}{900}\)
\(B=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{30^2}\)
\(B< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{29.30}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{29}-\frac{1}{30}\)
\(=1-\frac{1}{30}=\frac{29}{30}< 1\)
\(\Rightarrow A< 29\)
30 tháng 9 2020
So sánh C và D biết
C=1+13+13^2+...+13^13/1+13+13^2+...+13^12
D=1+11+11^2+...+11^13/1+11+11^2+...+11^12
TM
4 tháng 5 2018
\(a,\frac{7}{12}\cdot\frac{6}{11}+\frac{7}{12}\cdot\frac{5}{11}+2\frac{7}{12}\)
\(=\frac{7}{12}\cdot\left(\frac{6}{11}+\frac{5}{11}\right)+2\frac{7}{12}\)
\(=\frac{7}{12}+\frac{31}{12}\)
\(=\frac{38}{12}=\frac{19}{6}\)
\(b,\frac{-5}{9}\cdot\frac{-6}{13}+\frac{5}{-9}\cdot\frac{-5}{13}-\frac{5}{9}\)
\(=\frac{-5}{9}\cdot\frac{-6}{13}+\frac{-5}{9}\cdot\frac{-5}{13}+\frac{-5}{9}\cdot1\)
\(=\frac{-5}{9}\cdot\left(\frac{-6}{13}+\frac{-5}{13}+1\right)\)
\(=\frac{-5}{9}\cdot\left(\frac{-11}{13}+1\right)\)
\(=\frac{-5}{9}\cdot\frac{2}{13}\)
\(=\frac{-10}{117}\)
\(c,\)\(0,8\cdot\frac{-15}{14}-\frac{4}{5}\cdot\frac{13}{14}-1\frac{2}{5}\)
\(=\frac{4}{5}\cdot\frac{-15}{14}-\frac{4}{5}\cdot\frac{13}{14}-\frac{7}{5}\)
\(=\frac{4}{5}\cdot\left(\frac{-15}{14}-\frac{13}{14}\right)-\frac{7}{5}\)
\(=\frac{4}{5}\cdot\left(-2\right)-\frac{7}{5}\)
\(=\frac{-8}{5}-\frac{7}{5}\)
\(=-3\)
\(d,\)\(75\%\cdot\frac{6}{7}+5\%\cdot\frac{6}{7}+\frac{7}{10}\cdot1\frac{1}{7}\)
\(=\frac{3}{4}\cdot\frac{6}{7}+\frac{1}{20}\cdot\frac{6}{7}+\frac{7}{10}\cdot\frac{8}{7}\)
\(=\left(\frac{3}{4}+\frac{1}{20}\right)\cdot\frac{6}{7}+\frac{7}{10}\cdot\frac{8}{7}\)
\(=\frac{4}{5}\cdot\frac{6}{7}+\frac{4}{5}\cdot1\)
\(=\frac{4}{5}\cdot\left(\frac{6}{7}+1\right)\)
\(=\frac{4}{5}\cdot\frac{13}{7}\)
\(=\frac{52}{35}\)
chia từng hạng tử cho nhau