Tính
\(\frac{14^{1005}.5^{1006}}{2^{1007}.35^{1004}}\)
Ai nhanh mik cho 3k nè
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N
10 tháng 11 2018
\(\frac{14^{1005}.5^{1006}}{2^{1007}.35^{1004}}\)
\(=\frac{2^{1005}.7^{1005}.5^{1006}}{2^{1007}.5^{1004}.7^{1004}}\)
\(=\frac{5^2.7}{2^2}=\frac{25.7}{4}=\frac{175}{4}\)
10 tháng 11 2018
TRẦN TIỂU HY ƠI, BẠN TRÌNH BÀY RA GIÙM MK NHA. MK KO HIỂU LẮM
31 tháng 8 2021
\(\dfrac{1004}{1005}< \dfrac{1005}{1006}< \dfrac{1006}{1007}< \dfrac{1007}{1008}\)
HN
8 tháng 7 2018
\(\frac{\left(-5\right)^2.\left(-5\right)^3.16}{5^4.\left(-2\right)^4}=\frac{\left(-5\right)^5.16}{5^4.16}=\frac{\left(-5\right)^5}{5^4}=-5\)
\(\frac{14^{1005}.5^{1006}}{2^{1007}.35^{1004}}=\frac{14^{1005}.5^{1005}.5}{2^{1004}.2^3.35^{1004}}=\frac{\left(14.5\right)^{1005}.5}{\left(2.35\right)^{1004}.2^3}=\frac{70^{1005}.5}{70^{1004}.2^3}=\frac{70.5}{8}=\frac{350}{8}=\frac{175}{4}\)
Chúc bạn học tốt!
AK
8 tháng 7 2018
Toán lớp 6 ?
\(\frac{\left(-5\right)^2\left(-5\right)^3.16}{5^4.\left(-2\right)^4}=\frac{\left(-5\right)^5.2^4}{5^4.2^4}=-5\)
\(\frac{14^{1005}.5^{1006}}{2^{1007}.35^{1004}}=\frac{14^{1005}.5^{1005}.5}{2^{1004}.35^{1004}.2^3}=\frac{\left(14.5\right)^{1005}.5}{\left(2.35\right)^{1004}.8}=\frac{70^{1005}.5}{70^{1004}.8}=\frac{70.5}{8}=\frac{175}{4}\)
M
1
26 tháng 1 2021
Ta có: \(\dfrac{x+1006}{1007}+\dfrac{x+1005}{1008}=\dfrac{x+1004}{1009}+\dfrac{x+1003}{1010}\)
\(\Leftrightarrow\dfrac{x+1006}{1007}+1+\dfrac{x+1005}{1008}+1=\dfrac{x+1004}{1009}+1+\dfrac{x+1003}{1010}+1\)
\(\Leftrightarrow\dfrac{x+2013}{1007}+\dfrac{x+2013}{1008}=\dfrac{x+2013}{1009}+\dfrac{x+2013}{1010}\)
\(\Leftrightarrow\dfrac{x+2013}{1007}+\dfrac{x+2013}{1008}-\dfrac{x+2013}{1009}-\dfrac{x+2013}{1010}=0\)
\(\Leftrightarrow\left(x+2013\right)\left(\dfrac{1}{1007}+\dfrac{1}{1008}-\dfrac{1}{1009}-\dfrac{1}{1010}\right)=0\)
mà \(\dfrac{1}{1007}+\dfrac{1}{1008}-\dfrac{1}{1009}-\dfrac{1}{1010}\ne0\)
nên x+2013=0
hay x=-2013
Vậy: S={-2013}
MN
1
26 tháng 4 2018
Đặt \(A=\frac{1005}{1006}+\frac{1006}{1007}+\frac{1007}{1008}+\frac{1008}{1005}\) ta có :
\(A=\frac{1006-1}{1006}+\frac{1007-1}{1007}+\frac{1008-1}{1008}+\frac{1005+3}{1005}\)
\(A=\frac{1006}{1006}-\frac{1}{1006}+\frac{1007}{1007}-\frac{1}{1007}+\frac{1008}{1008}-\frac{1}{1008}+\frac{1005}{1005}+\frac{3}{1005}\)
\(A=1-\frac{1}{1006}+1-\frac{1}{1007}+1-\frac{1}{1008}+1+\frac{3}{1005}\)
\(A=\left(1+1+1+1\right)-\left(\frac{1}{1006}+\frac{1}{1007}+\frac{1}{1008}-\frac{3}{1005}\right)\)
\(A=4-\left(\frac{1}{1006}+\frac{1}{1007}+\frac{1}{1008}-\frac{1}{1005}-\frac{1}{1005}-\frac{1}{1005}\right)\)
\(A=4-\left[\left(\frac{1}{1006}-\frac{1}{1005}\right)+\left(\frac{1}{1007}-\frac{1}{1005}\right)+\left(\frac{1}{1008}-\frac{1}{1005}\right)\right]\)
Mà :
\(\frac{1}{1006}< \frac{1}{1005}\)\(\Rightarrow\)\(\frac{1}{1006}-\frac{1}{1005}< 0\) \(\left(1\right)\)
\(\frac{1}{1007}< \frac{1}{1005}\)\(\Rightarrow\)\(\frac{1}{1007}-\frac{1}{1005}< 0\) \(\left(2\right)\)
\(\frac{1}{1008}< \frac{1}{1005}\)\(\Rightarrow\)\(\frac{1}{1008}-\frac{1}{1005}< 0\) \(\left(3\right)\)
Từ (1), (2) và (3) suy ra :
\(\left(\frac{1}{1006}-\frac{1}{1005}\right)+\left(\frac{1}{1007}-\frac{1}{1005}\right)+\left(\frac{1}{1008}-\frac{1}{1005}\right)< 0\)
\(\Rightarrow\)\(A=4-\left[\left(\frac{1}{1006}-\frac{1}{1005}\right)+\left(\frac{1}{1007}-\frac{1}{1005}\right)+\left(\frac{1}{1008}-\frac{1}{1005}\right)\right]>4\)
\(\Rightarrow\)\(A>4\) ( điều phải chứng minh )
Vậy \(A>4\)
Chúc bạn học tốt ~
HT
1
6 tháng 12 2017
\(\dfrac{x-1001}{1006}+\dfrac{x-1003}{1004}+\dfrac{x-1005}{1002}+\dfrac{x-1007}{1000}=4\)
\(\Rightarrow\dfrac{x-1001}{1006}-1+\dfrac{x-1003}{1004}-1+\dfrac{x-1005}{1002}-1+\dfrac{x-1007}{1000}-1=0\)
\(\Rightarrow\dfrac{x-2007}{1006}+\dfrac{x-2007}{1004}+\dfrac{x-2007}{1002}+\dfrac{x-2007}{1000}=0\)
\(\Rightarrow\left(x-2007\right)\left(\dfrac{1}{1006}+\dfrac{1}{1004}+\dfrac{1}{1002}+\dfrac{1}{1000}\right)=0\)
Dễ thấy: \(\dfrac{1}{1000}+\dfrac{1}{1004}+\dfrac{1}{1002}+\dfrac{1}{1000}>0\Leftrightarrow x-2007=0\Leftrightarrow x=2007\)
\(\frac{2^{1005}.7^{1005}.5^{1006}}{2^{1007}.5^{1004}.7^{1004}}\)
\(=\frac{7.5^2}{2^2}\)
\(=\frac{175}{4}\)
Chúc bạn học tốt^^
\(\frac{2^{1005}.7^{1005}.5^{1006}}{2^{1007}.5^{1004}.7^{1004}}\)
\(=\frac{7.5^2}{2^2}\)
\(=\frac{175}{4}\)
Chúc bạn học tốt^^