Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a: =>4y+15/16=1
=>4y=1/16
=>y=1/64
b: =>10y+1/2+1/4+...+1/1024=1
=>10y+1023/1024=1
=>10y=1/1024
=>y=1/10240
\(\frac{4}{8.11}+\frac{4}{11.14}+...+\frac{4}{251.254}\)
\(=\frac{4}{3}\left(\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{251.254}\right)\)
\(=\frac{4}{3}\left(\frac{11-8}{8.11}+\frac{14-11}{11.14}+...+\frac{254-251}{251.254}\right)\)
\(=\frac{4}{3}\left(\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{251}-\frac{1}{254}\right)\)
\(=\frac{4}{3}\left(\frac{1}{8}-\frac{1}{254}\right)\)
\(=\frac{41}{254}\)
a: \(\Leftrightarrow\left(5x+\dfrac{3}{2}\right):\dfrac{8}{15}=\dfrac{25}{12}-\dfrac{5}{6}=\dfrac{25}{12}-\dfrac{10}{12}=\dfrac{15}{12}=\dfrac{5}{4}\)
\(\Leftrightarrow5x+\dfrac{3}{2}=\dfrac{5}{4}\cdot\dfrac{8}{15}=\dfrac{40}{60}=\dfrac{2}{3}\)
\(\Leftrightarrow5x=\dfrac{2}{3}-\dfrac{3}{2}=\dfrac{4-9}{6}=\dfrac{-5}{6}\)
hay x=-1/6
b: \(\Leftrightarrow\dfrac{1}{4}\left(2-\dfrac{1}{2}x\right)=\dfrac{5}{2}-\dfrac{1}{4}=\dfrac{10}{4}-\dfrac{1}{4}=\dfrac{9}{4}\)
=>2-1/2x=9
=>1/2x=-7
hay x=-14
c: \(\Leftrightarrow\left(x-7\right)^2=144\)
=>x-7=12 hoặc x-7=-12
=>x=19 hoặc x=-5
d: \(\Leftrightarrow4x+2=3x-15\)
hay x=-17
e: =>1/6x=-4
hay x=-24
x + 3 + 9 chia hết x + 3
9 chia hết x + 3
x + 3 thuộc Ư ( 9 )
mà Ư (9) = ( 1,3,9 )
hay x + 3 thuộc ( 1,3,9 )
ta có bảng
x + 3 1 3 9
x -2 0 6
ĐG Loại TM TM
Vậy x thuộc ( 0 , 6 )
a)\(\dfrac{2}{3}+\dfrac{1}{-4}-\dfrac{5}{18}=\dfrac{8}{12}-\dfrac{3}{12}-\dfrac{5}{18}=\dfrac{5}{18}-\dfrac{5}{18}=\dfrac{5}{36}\)
b)\(=\dfrac{5}{8}+\dfrac{3}{4}-\dfrac{9}{8}=\left(\dfrac{5}{8}-\dfrac{9}{8}\right)+\dfrac{3}{4}=--\dfrac{2}{4}+\dfrac{3}{4}=\dfrac{1}{4}\)
c)\(=\dfrac{6}{7}+\dfrac{1}{7}:\left(-\dfrac{21}{28}+\dfrac{24}{28}\right)=\dfrac{6}{7}+\dfrac{1}{7}\times\dfrac{28}{3}=\dfrac{6}{7}+\dfrac{4}{3}=\dfrac{46}{21}\)
e)\(=\dfrac{9}{17}-\dfrac{5}{13}-\dfrac{8}{13}+\dfrac{1}{17}=\left(\dfrac{9}{17}+\dfrac{1}{17}\right)+\left(-\dfrac{5}{13}-\dfrac{8}{13}\right)\)
\(=\dfrac{8}{17}-1=-\dfrac{9}{17}\)
\(x+xy=7\)
\(x\left(y+1\right)=7\)
=> x + 1 \(\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)
Lập bảng
x | 1 | -1 | 7 | -7 |
y + 1 | 7 | -7 | 1 | -1 |
y | 6 | -8 | 0 | -2 |
Sorry nãy máy load chậm
\(\frac{-101}{-100}=\frac{101}{100}>1\)
\(\frac{200}{201}< 1\)
\(\Rightarrow\frac{200}{201}< \frac{101}{100}\Rightarrow\frac{200}{201}< \frac{-101}{-100}\)
Bài 4:
a) \(4^{10}+4^7=4^7\left(4^3+1\right)=4^7.65⋮65\)
b) \(10^{10}-10^9-10^8=10^8\left(10^2-10-1\right)=10^8.89⋮89\)
Bài 5:
a) \(\Rightarrow n\inƯ\left(4\right)=\left\{-4;-2;-1;1;2;4\right\}\)
Do \(n\in N\)
\(\Rightarrow n\in\left\{1;2;4\right\}\)
b) \(\Rightarrow\left(n+2\right)+4⋮\left(n+2\right)\)
\(\Rightarrow\left(n+2\right)\inƯ\left(4\right)=\left\{-4;-2;-1;1;2;4\right\}\)
Do \(n\in N\)
\(\Rightarrow n\in\left\{0;2\right\}\)
c) \(\Rightarrow3\left(n-2\right)+7⋮\left(n-2\right)\)
\(\Rightarrow\left(n-2\right)\inƯ\left(7\right)=\left\{-7;-1;1;7\right\}\)
Do \(n\in N\)
\(\Rightarrow n\in\left\{1;3;9\right\}\)
d) \(\Rightarrow2\left(3n+9\right)⋮\left(2n-1\right)\)
\(\Rightarrow3\left(2n-1\right)+21⋮\left(2n-1\right)\)
\(\Rightarrow\left(2n-1\right)\inƯ\left(21\right)=\left\{-21;-7;-3;-1;1;3;7;21\right\}\)
Do \(n\in N\)
\(\Rightarrow n\in\left\{0;1;2;4;11\right\}\)
Bài 4
Ta có: \(4^{10}+4^7=4^7.4^3+4^7=4^7\left(4^3+1\right)=4^7.65\)
Vì \(65⋮65\) nên \(4^{10}+4^7⋮65\)
b) Ta có:\(10^{10}-10^9-10^8=10^8.10^2-10^8.10-10^8=10^8\left(10^2-10-1\right)=10^8.89\)
Vì \(89⋮89\) nên \(10^{10}-10^9-10^8⋮65\)