tìm x biết:
(1/3)2.x-1- (1/3)2=-2/27
mik cần lời giải chi tiết nhé và giải thích giúp mik nha.ai nhanh và đúng mik tick
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a) 2(x + 3) = 5(1 - x) - 2
<=> 2x + 6 = 5 - 5x - 2
<=> 2x + 6 = 3 - 5x
=> 2x - 5x = 6 + 3
=> -3x = 9
=> x = 9 : (-3)
=> x = -3
D = \(\dfrac{1}{1\times1981}\) + \(\dfrac{1}{2\times1982}\)+...+ \(\dfrac{1}{25\times2005}\)
D =\(\dfrac{1}{1980}\times\)( \(\dfrac{1980}{1\times1981}\)+ \(\dfrac{1980}{2\times1982}\)+....+ \(\dfrac{1980}{25\times2005}\))
D = \(\dfrac{1}{1980}\) \(\times\)(\(\dfrac{1}{1}\) - \(\dfrac{1}{1981}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{1982}\)+....+ \(\dfrac{1}{25}\) \(\times\) \(\dfrac{1}{2005}\))
D= \(\dfrac{1}{1980}\)[( \(\dfrac{1}{1}\) + \(\dfrac{1}{2}\) +....+ \(\dfrac{1}{25}\)) - ( \(\dfrac{1}{1981}\)+ \(\dfrac{1}{1982}\)+...+ \(\dfrac{1}{2005}\))]
E =\(\dfrac{1}{25}\times\)( \(\dfrac{1}{1\times26}\)+ \(\dfrac{1}{2\times27}\)+...+ \(\dfrac{1}{1980\times2005}\))
E = \(\dfrac{1}{25}\). (\(\dfrac{25}{1\times26}\) + \(\dfrac{25}{2\times27}\)+....+ \(\dfrac{25}{1980\times2005}\))
E = \(\dfrac{1}{25}\).(\(\dfrac{1}{1}\)-\(\dfrac{1}{26}\)+\(\dfrac{1}{2}\)-\(\dfrac{1}{27}\)+...+\(\dfrac{1}{1980}\)-\(\dfrac{1}{2005}\))
E=\(\dfrac{1}{25}\)[\(\dfrac{1}{1}\)+...+ \(\dfrac{1}{25}\)+ (\(\dfrac{1}{26}\)+...+\(\dfrac{1}{1980}\)) - (\(\dfrac{1}{26}\)+...+\(\dfrac{1}{1980}\)) - (\(\dfrac{1}{1981}\)+..\(\dfrac{1}{2005}\))]
E = \(\dfrac{1}{25}\) .[\(\dfrac{1}{1}\)+\(\dfrac{1}{2}\)+...+\(\dfrac{1}{25}\) - (\(\dfrac{1}{1981}\)+\(\dfrac{1}{1982}\)+...+ \(\dfrac{1}{2005}\))]
\(\dfrac{D}{E}\) = \(\dfrac{\dfrac{1}{1980}}{\dfrac{1}{25}}\) = \(\dfrac{5}{396}\)
tham khảo
Z1= 60 răng
Z2= 30 răng
a) Ta có: i= Z1/Z2
=> i=60/30=2
b) đĩa líp quay nhanh hơn vì có số răng ít hơn đia xích
1)5x+1 + 6.5x+1 = 875
5x+1 ( 1+6 ) = 875
5x+1 . 7 = 875
5x+1 = 875 : 7
5x+1 = 125
5x+1 = 53
x+1 = 3
x = 3 - 1
x = 2
2)3x+1 + 3x+3 = 810
3x . 3 + 32 . 3x+1 = 810
3x . 3 + 9 . 3x . 3 = 810
3x .3 ( 1 + 9 ) = 810
3x+1 . 10 = 810
3x+1 = 810 : 10
3x+1 = 81
3x+1 = 34
x+1 = 4
x = 4-1
x = 3
1. Tìm x
a) 1+2+3+...+x = 210
=> \(\frac{x\left(x+1\right)}{2}=210\)
=> x = 20
b) \(32.3^x=9.3^{10}+5.27^3\)
=>\(32.3^x=9.3^{10}+5.3^9\)(\(27^3=\left(3^3\right)^3=3^9\))
=>\(32.3^x=9.3.3^9+5.3^9\)
=>\(32.3^x=3^9\left(9.3+5\right)\)
=>\(32.3^x=3^9.32\)
=>x = 9
2.
Ta có 2A = 3A - A
=> 2A = \(3\left(1+3+3^2+3^3+....+3^{10}\right)\)\(-\)\(1-3-3^2-3^3-....-3^{10}\)
=> 2A = \(3+3^2+3^3+.....+3^{11}-\)\(1-3-3^2-3^3-...-3^{10}\)
=> 2A = \(3^{11}-1\)
=> 2A+1 = \(3^{11}-1+1\)=\(3^{11}\)
=> n = 11
Ta có : a)1 + 2 + 3 + ... + x = 210
=> \(\frac{x\left(x+1\right)}{2}=210\)
=> x(x + 1) = 420
=> x(x + 1) = 20.21
=> x = 20
b)\(\left(x-8\right)\left(x-2\right)=0\Leftrightarrow\orbr{\begin{cases}x-8=0\\x-2=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=8\\x=2\end{cases}}\)
c) \(\left(x+1\right)+\left(x+2\right)+...+\left(x+10\right)=9x+200\)
\(\Leftrightarrow\left(x+x+...+x\right)+\left(1+2+...+10\right)=9x+200\) (10 số hạng x)
\(\Leftrightarrow10x+55=9x+200\Leftrightarrow x+55=200\)
\(\Leftrightarrow x=145\)
Lời giải:
$(\frac{1}{3})^{2x-1}-\frac{1}{9}=\frac{-2}{27}$
$(\frac{1}{3})^{2x-1}=\frac{-2}{27}+\frac{1}{9}=\frac{1}{27}=(\frac{1}{3})^3$
$\Rightarrow 2x-1=3$
$\Rightarrow x=2$
(1/3)2x-1=1/9-2/27=1/27=(1/3)3
<-> 2x-1 = 3
2x=4
=>x=2