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Bài 1:
1 - 2 + 3 - 4 + .... + 2009 - 2010
= (1 - 2) + (3 - 4) + ... + (2009 - 2010)
= -1 . 1005
= -1005
Bài 2:
a) (15 - x) - (-x + 12) = 7 - (-5 + x)
=> 15 - x + x - 12 = 7 + 5 - x
=> -x + x + x = 7 + 5 - 15 + 12
=> x = 9
b) (x - 5)4 = (x - 5)6
=> x - 5 = 1 hoặc x - 5 = 0
=> x = 6 hoặc x = 5
c) (x + 1) + (x + 3) + ... + (x + 99) = 0
=> (x . 50) + (1 + 3 + ... + 99) = 0
=> (x . 50) + 2500 = 0
=> x . 50 = -2500
=> x = -50
\(a,-\frac{9}{12}=-\frac{9:3}{12:3}=-\frac{3}{4}\)
\(\frac{-18}{-24}=\frac{\left(-18\right):\left(-6\right)}{\left(-24\right):\left(-6\right)}=\frac{3}{4}\)
\(-\frac{35}{70}=-\frac{35:35}{70:35}=\frac{1}{2}\)
\(-\frac{9}{27}=-\frac{9:9}{27:9}=-\frac{1}{3}\)
\(b,\frac{1313}{4242}=\frac{1313:101}{4242:101}=\frac{13}{42}\)
\(\frac{-353535}{-424242}=\frac{\left(-353535\right):\left(-70707\right)}{\left(-424242\right):\left(-70707\right)}=\frac{5}{6}\)
\(c,\frac{2^3\times4^3\times5^4}{8^2\times25^3\times7}=\frac{2^3\times4^3\times25^2}{8\times8^2\times25^2\times25\times7}\) ( 4^3 = 8^2 ; 5^4 = 25^2 )
\(=\frac{1}{25\times7}=\frac{1}{175}\)
\(a.\frac{-9}{-12}=\frac{-9:3}{-12:3}=\frac{-3}{-4}.\)
\(\frac{-18}{-24}=\frac{-18:6}{-24:6}=\frac{-3}{-4}\)
\(\frac{-35}{-70}=\frac{-35:35}{-70:35}=\frac{-1}{-2}\)
\(\frac{-9}{-27}=\frac{-9:9}{-27:9}=\frac{-1}{-3}\)
A=5+52+...+52016
5A=52+53+...+52017
5A-A=(52+53+...+52017)-(5+52+...+52016)
4A = 52017 - 5
=> 4A + 5 = 52017 - 5 + 5 = 52017 = 5n-1
=> n-1=2017 => n=2018
A = 5 + 52 + 53 + ............ + 52016
5A = 52 + 53 + 54 + .............. + 52017
5A - A = ( 52 + 53 + 54 + ................ + 52017 ) - ( 5 + 52 + 53 + ................. + 52016 )
5A - A = 52 + 53 + 54 + ........... + 52017 - 5 - 52 - 53 - .............. - 52016
4A = 52017 - 5
4A + 5 = 5n-1
\(\Rightarrow\) 4A + 5 = 52017 - 5 + 5 = 52017 = 5n-1
\(\Rightarrow\) n - 1 = 2017
\(\Rightarrow\) n = 2018
Vậy n = 2018
\(7-5\left(x-2\right)=3+2\left(4-x\right)\)
\(\Leftrightarrow7-5x+10=3+8-2x\)
\(\Leftrightarrow17+5x=11-2x\)
\(\Leftrightarrow17-11=-2x-5x\)
\(\Leftrightarrow6=-7x\)
\(\Leftrightarrow x=\frac{-7}{6}\)
7 - 5( x - 2) = 3 + 2 (4-x )
=> 7 - 5x + 10 = 3 + 8 - 2x
=> 17 + 5x = 11 - 2x
=> 17 - 11 = -2x - 5x
=>6 = -7x
=> x = -7/6
Vay x = -7/6
Chuc ban hc tot