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\(\left(x+1\right)\left(21-1\right)=-21\)
\(\left(x+1\right)\cdot20=-21\)
\(x+1=\frac{-21}{20}\)
\(x=\frac{-21}{20}-1\)
\(x=\frac{-41}{20}\)
( x + 1 ) . ( 21 - 1 ) = -21
( x + 1 ) . 20 = -21
( x + 1 ) = -21 : 20
( x + 1 ) = 1.05
x = 1,05 - 1
x = - 0 ,05
\(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{2}{x\left(x+1\right)}=\frac{2010}{2012}\)
\(\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{x\left(x+1\right)}=\frac{2010}{2012}\)
\(\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+...+\frac{2}{x\left(x+1\right)}=\frac{2010}{2012}\)
\(2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2010}{2012}\)
\(2\left(\frac{1}{4}-\frac{1}{x+1}\right)=\frac{2010}{2012}\)
\(\frac{1}{4}-\frac{1}{x+1}=\frac{2010}{2012}\div2\)
\(\frac{1}{4}-\frac{1}{x+1}=\frac{1005}{2012}\)
\(\frac{1}{x+1}=\frac{1}{4}-\frac{1005}{2012}\)
\(\frac{1}{x+1}=\frac{-502}{2012}=-\frac{251}{1006}\)
\(\Rightarrow x+1=1\div-\frac{251}{1006}=-\frac{1006}{251}\)
\(x=\frac{-1006}{251}-1=-\frac{1257}{251}\)
a) (x - 3)(y - 3) = 9 = 1.9 = 3.3
Lập bảng:
x - 3 | 1 | -1 | 3 | -3 | 9 | -9 |
y - 3 | 9 | -9 | 3 | -3 | 1 | -1 |
x | 4 | 2 | 6 | 0 | 12 | -3 |
y | 12 | -6 | 6 | 0 | 4 | 2 |
Vậy ...
b) A = \(\frac{10^{19}+1}{10^{20}+1}\) => 10A = \(\frac{10^{20}+10}{10^{20}+1}=1+\frac{9}{10^{20}+1}\)
B = \(\frac{10^{20}+1}{10^{21}+1}\) => 10B = \(\frac{10^{21}+10}{10^{21}+1}=1+\frac{9}{10^{21}+1}\)
Do \(10^{20}+1< 10^{21}+1\) => \(\frac{9}{10^{20}+1}>\frac{9}{10^{21}+1}\) => 10A > 10B => A > B
\(x\) + \(\dfrac{1}{10}\) + \(x\) + \(\dfrac{1}{11}\) = \(x\) + \(\dfrac{1}{21}\)
\(x+x-x\) = \(\dfrac{1}{21}\) - \(\dfrac{1}{10}\) - \(\dfrac{1}{11}\)
\(x\) = - \(\dfrac{331}{2310}\)
\(x+\dfrac{1}{10}+x+\dfrac{1}{11}=x+\dfrac{1}{21}\)
\(x+x-x=\dfrac{1}{21}-\dfrac{1}{10}-\dfrac{1}{11}\)
\(x=\dfrac{-11}{210}-\dfrac{1}{11}\)
\(x=\dfrac{-331}{2310}\)
\(x\) + \(\dfrac{1}{10}\) + \(x\) + \(\dfrac{1}{10}\) = \(x\) + \(\dfrac{1}{21}\)
\(x+x\) - \(x\) = \(\dfrac{1}{21}\) - \(\dfrac{1}{10}\) - \(\dfrac{1}{10}\)
\(x\) = \(\dfrac{1}{21}\) - \(\dfrac{1}{5}\)
\(x\) = - \(\dfrac{16}{105}\)