[ 2 . x - 1 ] + [ 2 . x -2 ] + ... + [ 2 . x -10 ] =45
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H
10 tháng 7 2023
`2 1/2 xx 7/5 + (-9/10) xx 2/3`
`= 5/2 xx 7/10 + (-9/10) xx 2/3`
`= 35/20 + (-18/30)`
`= 7/4 + (-3/5)`
`= 23/20`
__
`x + 45% =2 1/2 - 5/3`
`=> x+ 45/100 = 5/2 - 5/3`
`=>x+ 9/20= 15/6-10/6`
`=> x+9/20 = 5/6`
`=>x= 5/6 - 9/20`
`=>x=23/60`
__
`80% +x=-5/2 +3/4`
`=> 80/100 + x= -10/4 +3/4`
`=> 4/5 + x= -7/4`
`=>x= -7/4-4/5`
`=>x=-51/20`
__
`4/25 -x=-5/2 +(-3/10)`
`=> 4/25 -x= -25/10 +(-3/10)`
`=> 4/25 -x= -28/10`
`=>x= 4/25 -(14/5)`
`=>x= 4/25 + 14/5`
`=>x=74/25`
20 tháng 12 2022
a: =25(15+45*3)
=25*150
=3750
b: \(=-10\left(25+75-50\right)=-10\cdot50=-500\)
c: =>3^x-2=27
=>x-2=3
=>x=5
d: =>2x-5=-4
=>2x=1
=>x=1/2
e: =>2(x-1)^2=32
=>(x-1)^2=16
=>x-1=4 hoặc x-1=-4
=>x=-3 hoặc x=5
f: =>25(x+3)=75
=>x+3=3
=>x=0
BN
20 tháng 5 2018
Bài 1:
\(A=\frac{1}{\left(1+2\right)}+\frac{1}{\left(1+2+3\right)}+\frac{1}{\left(1+2+3+4\right)}\)\(+\frac{1}{\left(1+2+3+4+5\right)}+...+\)\(\frac{1}{\left(1+2+3+...+10\right)}\)
\(A=\frac{1}{3}+\frac{1}{6}+....+\frac{1}{55}\)
\(A=2\left(\frac{1}{6}+\frac{1}{12}+....+\frac{1}{110}\right)\)
\(A=2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{10}-\frac{1}{11}\right)\)
\(A=2.\left(\frac{1}{2}-\frac{1}{11}\right)\)
\(A=\frac{9}{11}\)
Bài 2 :
2) Tử số = 11 x 13 x 15 + 3 x 3 x 3 x 11 x 13 x 15 + 5 x 5 x 5 x 11 x 13 x 15 + 9 x 9 x 9 x 11 x 13 x 15
= (1 + 3 x 3 x 3 + 5 x 5 x 5 + 9 x 9 x9) x 11 x 13 x 15 = (1+27+125+ 729) x 11 x 13 x 15
Mẫu số = 11 x 13 x 17 + 3 x 3 x 3 x 13 x 15 x 19 + 5 x 5 x 5 x 13 x 15 x 17 + 9 x 9 x 9 x 13 x 15 x 17 lớn hơn 11 x 13 x 15 + 3 x 3 x 3 x 13 x 15 x 17 + 5 x 5 x 5 x 13 x 15 x 17 + 9 x 9 x 9 x 13 x 15 x 17
= (1 + 3 x 3 x 3 + 5 x 5 x 5 + 9 x 9 x9) 13 x 15 x 17 = (1+27+125+729) x 13 x 15 x 17
\(\Rightarrow A< \frac{\left(1+27+125+729\right)\times11\times13\times15}{\left(1+27+125+729\right)\times13\times15\times17}\)
\(=\frac{11}{17}\)
\(=\frac{1111}{1717}=B\)
Vậy \(A=B\)
2 tháng 2 2021
\(a,80-\left(10x-5\right)=45\\ \Rightarrow80-10x+5=45\\ \Rightarrow-10x=-40\\ \Rightarrow x=4\)
\(b,\left(x+1\right)\left(x-2\right)=0\\ \Rightarrow\left[{}\begin{matrix}x+1=0\\x-2=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-1\\x=2\end{matrix}\right.\)
\(c,\left|5+5x\right|=2^2.5\\ \Rightarrow\left|5+5x\right|=20\\ \Rightarrow\left[{}\begin{matrix}5+5x=20\\5+5x=-20\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}5x=15\\5x=-25\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=3\\x=-5\end{matrix}\right.\)
\(d,-10-\left(-5\right)+\left(3-x\right)=-8\\ \Rightarrow-10+5+3-x=-8\\ \Rightarrow-x=-6\\ \Rightarrow x=6\)
2 tháng 2 2021
a) 80-(10x-5)=45
=> 80 - 10 x + 5 =45
=>-10x = -40
=>x=4
b)(x+1)×(x-2)=0
\(\Rightarrow\left[{}\begin{matrix}x+1=0\\x=2+0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-1\\x=2\end{matrix}\right.\)
c) |5+5x|=2^2×5
=>|5+5x|=20
\(\Rightarrow\left[{}\begin{matrix}5+5x=-20\\5+5x=20\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-5\\x=3\end{matrix}\right.\)
d) -10-(-5)+(3-x)=-8
=>-10+5 +3-x=-8
=>2+x=8
=>x=6
MH
3 tháng 3 2023
\(\dfrac{45}{135}=\dfrac{45:45}{135:45}=\dfrac{1}{3}\)
\(\dfrac{117}{234}=\dfrac{117:117}{234:117}=\dfrac{1}{2}\)
\(\dfrac{1515}{2727}=\dfrac{1515:303}{2727:303}=\dfrac{5}{9}\)
\(\dfrac{232323}{494949}=\dfrac{232323:10101}{494949:10101}=\dfrac{23}{49}\)
\(\left(x-\dfrac{1}{3}\right)+\dfrac{1}{4}=\dfrac{1}{2}\)
\(x-\dfrac{1}{3}=\dfrac{1}{2}-\dfrac{1}{4}\)
\(x-\dfrac{1}{3}=\dfrac{2}{4}-\dfrac{1}{4}\)
\(x-\dfrac{1}{3}=\dfrac{1}{4}\)
\(x=\dfrac{1}{4}+\dfrac{1}{3}\)
\(x=\dfrac{3}{12}+\dfrac{4}{12}\)
\(x=\dfrac{7}{12}\)
\(x-\left(\dfrac{1}{7}+\dfrac{2}{5}\right)=\dfrac{16}{35}\)
\(x-\left(\dfrac{5}{35}+\dfrac{14}{35}\right)=\dfrac{16}{35}\)
\(x-\dfrac{19}{35}=\dfrac{16}{35}\)
\(x=\dfrac{16}{35}+\dfrac{19}{35}\)
\(x=\dfrac{35}{35}\)
\(x=1\)
\(x+\dfrac{3}{7}=\dfrac{2}{5}+\dfrac{3}{10}\)
\(x+\dfrac{3}{7}=\dfrac{4}{10}+\dfrac{3}{10}\)
\(x+\dfrac{3}{7}=\dfrac{7}{10}\)
\(x=\dfrac{7}{10}-\dfrac{3}{7}\)
\(x=\dfrac{49}{70}-\dfrac{30}{70}\)
\(x=\dfrac{19}{30}\)
AM
13 tháng 6 2015
1)\(A=\frac{1}{3}+\frac{1}{6}+...+\frac{1}{55}=2\left(\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)=2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}\right)=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)=2.\left(\frac{1}{2}-\frac{1}{11}\right)=\frac{9}{11}\)
13 tháng 6 2015
2) Tử số = 11 x 13 x 15 + 3 x 3 x 3 x 11 x 13 x 15 + 5 x 5 x 5 x 11 x 13 x 15 + 9 x 9 x 9 x 11 x 13 x 15
= (1 + 3 x 3 x 3 + 5 x 5 x 5 + 9 x 9 x9) x 11 x 13 x 15 = (1+27+125+ 729) x 11 x 13 x 15
Mẫu số = 11 x 13 x 17 + 3 x 3 x 3 x 13 x 15 x 19 + 5 x 5 x 5 x 13 x 15 x 17 + 9 x 9 x 9 x 13 x 15 x 17
lớn hơn 11 x 13 x 15 + 3 x 3 x 3 x 13 x 15 x 17 + 5 x 5 x 5 x 13 x 15 x 17 + 9 x 9 x 9 x 13 x 15 x 17
= (1 + 3 x 3 x 3 + 5 x 5 x 5 + 9 x 9 x9) 13 x 15 x 17 = (1+27+125+729) x 13 x 15 x 17
=> \(A<\frac{\left(1+27+125+729\right)\times11\times13\times15}{\left(1+27+125+729\right)\times13\times15\times17}=\frac{11}{17}=\frac{1111}{1717}=B\)
Vậy A < B
Y
7 tháng 7 2023
\(9,\left(2x-5\right)^2-\left(x+1\right)^2=0\\ \Leftrightarrow\left(2x-5-x-1\right)\left(2x-5+x+1\right)=0\)
\(\Leftrightarrow\left(x-6\right)\left(3x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-6=0\\3x-4=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=6\\x=\dfrac{4}{3}\end{matrix}\right.\)
Vậy \(S=\left\{6;\dfrac{4}{3}\right\}\)
\(10,\left(x+3\right)^2-x^2=45\)
\(\Leftrightarrow x^2+6x+9-x^2-45=0\\ \Leftrightarrow6x=36\\ \Leftrightarrow x=6\)
Vậy \(S=\left\{6\right\}\)
\(11,\left(5x-4\right)^2-49x^2=0\\ \Leftrightarrow\left(5x-4\right)^2-\left(7x\right)^2=0\\ \Leftrightarrow\left(5x-4-7x\right)\left(5x-4+7x\right)=0\\ \Leftrightarrow\left(-2x-4\right)\left(12x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}-2x-4=0\\12x-4=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=\dfrac{1}{3}\end{matrix}\right.\)
Vậy \(S=\left\{-2;\dfrac{1}{3}\right\}\)
\(12,16\left(x-1\right)^2-25=0\\ \Leftrightarrow4^2\left(x-1\right)^2-5^2=0\\ \Leftrightarrow\left[4\left(x-1\right)\right]^2-5^2=0\\ \Leftrightarrow\left(4x-4\right)^2-5^2=0\\ \Leftrightarrow\left(4x-4-5\right)\left(4x-4+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}4x-9=0\\4x+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{9}{4}\\x=-\dfrac{1}{4}\end{matrix}\right.\)
Vậy \(S=\left\{-\dfrac{1}{4};\dfrac{9}{4}\right\}\)
\(\left(2x-1\right)+\left(2x-2\right)+...+\left(2x-10\right)=45\)
\(\left(2x+2x+...+2x\right)-\left(1+2+3+...+10\right)=45\)( có 10 số 2x )
\(20x-45=45\)
\(20x=45+45\)
\(20x=90\)
\(x=\frac{90}{20}\)
\(x=\frac{9}{2}\)
Vậy \(x=\frac{9}{2}\)