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C=5/1.2+5/2.3+5/3.4+...+5/99.100
C=5.(1/1.2+1/2.3+1/3.4+...+1/99.100)
C=5.(1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100)
C=5.(1-1/100)
C=5.(100/100-1/100)
C=5.9/100
C=9/20
Chúc bạn học tốt nha, Lan Anh
\(C=\frac{5}{1.2}+\frac{5}{2.3}+\frac{5}{3.4}+....+\frac{5}{99.100}\)
\(C=5.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+......+\frac{1}{99.100}\right)\)
\(C=5.\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+......+\frac{1}{99}-\frac{1}{100}\right)\)
\(C=5.\left(\frac{1}{1}-\frac{1}{100}\right)=5.\frac{99}{100}=\frac{99}{20}\)
Vậy C=99/20
5 . 3 - 5 . x - 2 . x - 2 . 4 = -4
15 - 5 . x - 2 .x -8 =-4
15 - 5 .x - 2. x = -4 + 8
15 - 5 . x -2 . x = 4
5 . x - 2 .x = 15 - 4
x.( 5 - 2) =9
x. 3 9
x = 9 /3
x =3
1) \(x^2+\frac{8}{9}=\frac{41}{36}\)\(\Leftrightarrow x^2=\frac{1}{4}\Leftrightarrow x=\pm\frac{1}{2}\)
2) \(\left(x-3\right)^2+-\frac{9}{25}=\frac{2}{5}.\frac{8}{5}\)
\(\Leftrightarrow\left(x-3\right)^2=1\)
\(\Leftrightarrow\orbr{\begin{cases}x-3=1\\x-3=-1\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=4\\x=2\end{cases}}\)
3) \(\frac{3}{11}.\frac{22}{6}-\left(x-1\right)^2=\frac{7}{16}\)
\(\Leftrightarrow\left(x-1\right)^2=\frac{9}{16}\)
\(\Leftrightarrow\orbr{\begin{cases}x-1=\frac{3}{4}\\x-1=-\frac{3}{4}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{7}{4}\\x=\frac{1}{4}\end{cases}}\)
4) \(1+\left(x+1\right)^3=\frac{37}{64}\)
\(\Leftrightarrow\left(x+1\right)^3=-\frac{27}{64}\)
\(\Rightarrow x+1=-\frac{3}{4}\)
\(\Leftrightarrow x=-\frac{7}{4}\)
5) \(\left(x-\frac{1}{2}\right)^2-\frac{9}{16}=1\)
\(\Leftrightarrow\left(x-\frac{1}{2}\right)^2=\frac{25}{16}\)
\(\Leftrightarrow\orbr{\begin{cases}x-\frac{1}{2}=\frac{5}{4}\\x-\frac{1}{2}=-\frac{5}{4}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{7}{4}\\x=-\frac{3}{4}\end{cases}}\)
6) Bn ghi rõ đề nha mk ko hiểu
6 ) \(\frac{3-x}{5-x}=\left(\frac{-3}{5}\right)^2\)
\(\frac{3-x}{5-x}=\frac{9}{25}\Leftrightarrow\frac{3-x}{5-x}-\frac{9}{25}\Leftrightarrow\frac{75-25x}{125-25x}-\frac{45-9x}{125-5x}=0\)
\(\Rightarrow\frac{75-25-45+9x}{125-25x}=0\Leftrightarrow5+9x=0\Leftrightarrow x=\frac{-5}{9}\)
\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+..+\frac{1}{x\left(x+2\right)}=\frac{20}{41}\)
\(\frac{1}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{x.\left(x+2\right)}\right)=\frac{20}{41}\)
\(\frac{1}{2}\left(\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{\left(x+2\right)-x}{x\left(x+2\right)}\right)=\frac{20}{41}\)
\(\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{20}{41}\)
\(\frac{1}{2}\left(1-\frac{1}{x+2}\right)=\frac{20}{41}\)
\(1-\frac{1}{x+2}=\frac{20}{41}:\frac{1}{2}\)
\(1-\frac{1}{x+2}=\frac{40}{41}\)
\(\frac{1}{x+2}=1-\frac{40}{41}\)
\(\frac{1}{x+2}=\frac{1}{41}\)
\(x+2=41\)
\(x=41-2\)
\(x=39\)
Tìm x
a) \(\frac{1}{1\times3}+\frac{1}{3\times5}+\frac{1}{5\times7}+...+\frac{1}{x\times\left(x+2\right)}=\frac{20}{41}\)
\(\Rightarrow\frac{1}{2}\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{x\times\left(x+1\right)}\right)=\frac{20}{41}\)
\(\Rightarrow\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{x\times\left(x+2\right)}=\frac{20}{41}:\frac{1}{2}\)
\(\Rightarrow\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{x\times\left(x+2\right)}=\frac{40}{41}\)
\(\Rightarrow1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{\left(x+2\right)}=\frac{40}{41}\)
\(\Rightarrow1-\frac{1}{x+2}=\frac{40}{41}\)
\(\Rightarrow\frac{1}{x+2}=1-\frac{40}{41}\)
\(\Rightarrow\frac{1}{x+2}=\frac{1}{41}\)
\(\Rightarrow x+2=41\)
\(\Rightarrow x=41-2\)
\(\Rightarrow x=39\)
Vậy x = 39
a) (-2) . ( x+7 ) + (-5) = 7
<=>(-2).(x+7)=7+5
<=>x+7=12:(-2)
<=>x+7=-6
<=>x=(-6)-7
<=>x=-13
Vậy x=-13
b)(x+4) : (-7) = 14
<=>x+4=14 x (-7)
<=>x+4=-98
<=>x=-98-4
<=>x=-102
Vậy x= -102
c) 72 : ( x+5) - 4 = -12
<=>72:(x+5)=(-12)+4
<=>x+5=72:(-8)
<=>x+5=-9
<=>x=-9-5
<=>x=-14
Vậy x= -14
d) (x+3) : (-6 ) + 12 = 8
<=>(x+3) :(-6)=8-12
<=>x+3=(-4)x(-6)
<=>x+3=24
<=>x=24-3
<=>x=21
Vậy x= 21
\(\frac{2}{3}x:\frac{1}{5}=\frac{4}{3}:25\%\)
\(\frac{2}{3}x:\frac{1}{5}=\frac{4}{3}:\frac{1}{4}=\frac{16}{3}\)
\(\frac{2}{3}x=\frac{16}{3}.\frac{1}{5}=\frac{16}{15}\)
\(x=\frac{16}{15}:\frac{2}{3}=\frac{8}{5}\)
Vậy x=8/5
dễ nhưng dài