Tìm x:
a) \(\frac{1}{3}\). x +\(\frac{2}{5}\). (x-1) =4
b)3\(^{x-1}\) + \(\frac{5}{2}\). 3\(^x\)=162
Tính :
1.2+2.3+3.4+...+2015.2016
Các bạn làm nhanh nha mai cô giáo mk kiểm tra òi
K
Khách
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Những câu hỏi liên quan
10 tháng 4 2017
Ta có : \(\frac{x-1}{2}=\frac{x+1}{3}\)
<=> \(3\left(x-1\right)=2\left(x+1\right)\)
<=> \(3x-3=2x+2\)
<=> \(3x-2x=2+3\)
<=> x = 5
S
10 tháng 4 2017
a, \(\frac{x-1}{2}=\frac{x+1}{3}\)
=> (x-1)3 = 2(x+1)
=> 3x - 3 = 2x + 2
=> 3x - 2x = 2 + 3
=> x = 5
b, \(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{100}=\frac{99}{100}< 1\) (ĐPCM)
4 tháng 4 2017
\(\left(3\frac{1}{2}+2x\right).2\frac{2}{3}=5\frac{1}{3}\)
<=>\(\left(\frac{7}{2}+2x\right).\frac{8}{3}=\frac{16}{3}\)
<=>\(\frac{28}{3}+\frac{16x}{3}=\frac{16}{3}\)
<=>\(\frac{16x}{3}=\frac{-2}{3}\)
<=>\(16x=-2\)
<=>\(x=\frac{-1}{8}\)
vậy \(x=\frac{-1}{8}\)
b,\(\left|2x+3\right|=5\)
xét x<0,ta co: \(\left|2x+3\right|=5\)<=> \(-2x+3=5\)<=>\(-2x=2\)<=>\(x=-1\)(loại)
xét x>0,ta co:\(\left|2x+3\right|=5\)<=>\(2x+3=5\)<=>\(2x=2\)<=>\(x=1\)
c,\(\frac{x-2}{4}=\frac{5+x}{3}\)
<=>\(\frac{3x-6}{12}=\frac{20+4x}{12}\)
=>\(3x-6=20+4x\)
<=>\(3x-6-20-4x=0\)
<=>\(-x-26=0\)
<=>\(-x=26\)
<=>\(x=-26\)
kl:.......
AW
4 tháng 4 2018
b) \(\frac{1^2}{1\cdot2}\cdot\frac{2^2}{2\cdot3}\cdot\frac{3^2}{3\cdot4}\cdot...\cdot\frac{100^2}{100\cdot101}=\frac{\left(1\cdot2\cdot3\cdot...\cdot100\right)}{1\cdot2\cdot3\cdot4\cdot...\cdot100}\cdot\frac{\left(1\cdot2\cdot3\cdot...\cdot100\right)}{2\cdot3\cdot4\cdot...\cdot101}=1\cdot\frac{1}{101}=\frac{1}{101}\)
a không biết
H
16 tháng 3 2023
\(\dfrac{x-1}{x}-\dfrac{1}{x+1}=\dfrac{2x-1}{x^2+x}\)
\(\Leftrightarrow\dfrac{x-1}{x}-\dfrac{1}{x+1}=\dfrac{2x-1}{x\left(x+1\right)}\)
ĐKXĐ : \(\left\{{}\begin{matrix}x\ne0\\x+1\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne0\\x\ne-1\end{matrix}\right.\)
Ta có : `(x-1)/x -1/(x+1) =(2x-1)/(x(x+1))`
\(\Leftrightarrow\dfrac{\left(x-1\right)\left(x+1\right)}{x\left(x+1\right)}-\dfrac{x}{x\left(x+1\right)}=\dfrac{2x-1}{x\left(x+1\right)}\)
`=> x^2 +x -x-1 -x-2x+1=0`
`<=> x^2 -3x =0`
`<=> x(x-3)=0`
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(ktm\right)\\x=3\end{matrix}\right.\)
__
`(x+2)(5-3x)=0`
\(\Leftrightarrow\left[{}\begin{matrix}x+2=0\\5-3x=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-2\\3x=5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=\dfrac{5}{3}\end{matrix}\right.\)
__
\(\dfrac{5\left(1-2x\right)}{3}+\dfrac{x}{2}=\dfrac{3\left(x-5\right)}{4}-2\)
\(\Leftrightarrow\dfrac{20\left(1-2x\right)}{12}+\dfrac{6x}{12}=\dfrac{9\left(x-5\right)}{12}-\dfrac{24}{12}\)
`<=> 2x- 40x + 6x = 9x - 45 -24`
`<=> 2x- 40x + 6x-9x + 45 +24=0`
`<=>-41x+69=0`
`<=>-41x=-69`
`<=> x=69/41`
16 tháng 3 2023
a:=>x^2-1-x=2x-1
=>x^2-x-1=2x-1
=>x^2-3x=0
=>x=0(loại) hoặc x=3(nhận)
b:=>x+2=0 hoặc 5-3x=0
=>x=-2 hoặc x=5/3
c:=>20(1-2x)+6x=9(x-5)-24
=>20-40x+6x=9x-45-24
=>-34x+20=9x-69
=>-43x=-89
=>x=89/43
d: =>x^2+4x+4-x^2-2x+3=2x^2+8x-4x-16-3
=>2x^2+4x-19=-2x+7
=>2x^2+6x-26=0
=>x^2+3x-13=0
=>\(x=\dfrac{-3\pm\sqrt{61}}{2}\)
e: =>(2x-3)(2x-3-x-1)=0
=>(2x-3)(x-4)=0
=>x=4 hoặc x=3/2
HN
17 tháng 3 2018
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+..........+\frac{1}{19.20}-\frac{x}{40}=\frac{3}{-10}\)
\(\Rightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-........-\frac{1}{20}-\frac{x}{40}=\frac{-3}{10}\)
\(\Rightarrow1-\frac{1}{20}-\frac{x}{40}=\frac{-3}{10}\)
\(\Rightarrow\frac{40}{40}-\frac{2}{40}-\frac{x}{40}=\frac{-12}{40}\)
\(\Rightarrow\frac{38}{40}-\frac{x}{40}=\frac{-12}{40}\)
\(\Rightarrow\frac{x}{40}=\frac{38}{40}-\frac{-12}{40}\)
\(\Rightarrow\frac{x}{40}=\frac{38}{40}+\frac{12}{40}\)
\(\Rightarrow\frac{x}{40}=\frac{50}{40}\)
\(\Rightarrow x=50\)
Vậy x = 50
EG
17 tháng 3 2018
\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+..+\frac{1}{19\cdot20}-\frac{x}{40}=\frac{-3}{10}\)\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+..+\frac{1}{19}-\frac{1}{20}-\frac{x}{40}=\frac{3}{-10}\)
\(1-\frac{1}{20}-\frac{x}{40}=\frac{3}{-10}\)
\(\frac{x}{40}=1-\frac{1}{20}-\frac{3}{-10}=1\frac{1}{4}=\frac{5}{4}\)
\(\frac{x}{40}=\frac{5}{4}\Rightarrow x=\frac{40\cdot5}{4}=50\)
26 tháng 3 2017
1.
1.2 +2.3 +...+97.98
=1/3.(1.2.3 +2.3.3 +3.4.3 +...+97.98.3)
=1/3.(1.2.3 - 0.1.2+ 2.3.4 -1.2.3 + 3.4.5 -2.3.4 + ... +97.98.99 -96.97.98)
=1/3 . 97.98.99
= 313698
=>1.2 +2.3 +...+97.98-x=16
=>313698-x=16
=> x=313682
4.
\(\left[\left(\frac{36}{x}-x\right):x-x\right]:x-x=-x\)
\(\left[\left(\frac{36}{x}-x\right):x-x\right]:x=-x+x\)
\(\left[\left(\frac{36}{x}-x\right):x-x\right]:x=0\)
\(\left[\left(\frac{36}{x}-x\right):x-x\right]=0\)
\(\left(\frac{36}{x}-x\right):x=x\Rightarrow\frac{36}{x}-x=x^2\)
\(\frac{36}{x}=x^2+x=x\left(x+1\right)\Rightarrow36=x^2\left(x+1\right)\)
Mà Ư(36)={1;2;3;4;6;9;12;18;36}; 9 là số chính phương duy nhất bé hơn 36=> x2 = 9 => x=3
2 câu kia thì đợi một lúc.
NW
3
K
13 tháng 11 2018
\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\frac{2.\left(y-2\right)}{6}=\frac{3.\left(z-3\right)}{12}\)
áp dụng t.c dãy tỉ số bằng nhau ta có:
\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}=\frac{2y-4}{6}=\frac{3z-9}{12}=\frac{x-1-2y+4+3z-9}{4-6+12}=1\)
\(\frac{x-1}{2}=1\Rightarrow x-1=2\Rightarrow x=3\)
\(\frac{y-2}{3}=1\Rightarrow y-2=3\Rightarrow y=5\)
\(\frac{z-3}{4}=1\Rightarrow z-3=4\Rightarrow z=7\)
Vậy x=3,y=5,z=7