Bài 4: Tính hợp lí
\(\frac{3}{11x13}\)+ \(\frac{3}{13x15}\)+ \(\frac{3}{15x17}\)+ \(\frac{3}{17x19}\)+ \(\frac{3}{19x21}\)
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Tìm x,y thuộc Z
a,\(\frac{x}{10}-\frac{1}{y}=\frac{13}{10}\)
b,\(\frac{1}{x}+\frac{y}{2}=\frac{5}{8}\)
\(\left(x-4\right)^2=\left(x-4\right)^4\)
\(\Rightarrow\left(x-4\right)^2-\left(x-4\right)^4=0\)
\(\Rightarrow\left(x-4\right)^2-\left(x-4\right)^2.\left(x-4\right)^2=0\)
\(\Rightarrow\left(x-4\right)^2.\left[1-\left(x-4\right)^2\right]=0\)
TH 1 : \(\left(x-4\right)^2=0\Rightarrow x-4=0\Rightarrow x=4\)
TH 2 : \(1-\left(x-4\right)^2=0\Rightarrow\left(x-4\right)^2=1\Rightarrow\orbr{\begin{cases}x-4=1\\x-4=-1\end{cases}}\Rightarrow\orbr{\begin{cases}x=5\\x=3\end{cases}}\)
Vậy x = 3; x = 4 hoặc x = 5
M = \(\frac{1}{5}+\left(\frac{1}{5}\right)^2+\left(\frac{1}{5}\right)^3+...+\left(\frac{1}{5}\right)^{^{^{ }}50}\)
=> 5M = 1 + \(\frac{1}{5}+\left(\frac{1}{5}\right)^2+...+\left(\frac{1}{5}\right)^{49}\)
=> 5M - M = ( 1 + \(\frac{1}{5}+\left(\frac{1}{5}\right)^2+...+\left(\frac{1}{5}\right)^{49}\)) - ( \(\frac{1}{5}+\left(\frac{1}{5}\right)^2+\left(\frac{1}{5}\right)^3+...+\left(\frac{1}{5}\right)^{^{^{ }}50}\))
4M = 1 - \(\left(\frac{1}{5}\right)^{50}\)
=> M = \(\frac{1-\left(\frac{1}{5}\right)^{50}}{4}\)< \(\frac{1}{4}\)
a) 106 - 57
= 56 . ( 26 - 5 )
= 56 . ( 64 - 5 )
= 56 . 59 \(⋮\)59
b ) 87 - 218
= 47 . 27 - 218
= 27 . ( 47 - 211 )
= 27 . 14 336
= 27 . 14 . 1024 \(⋮\)14 ( dpcm )
\(\frac{3}{11\text{x}13}+\frac{3}{13\text{x}15}+\frac{3}{15\text{x}17}+\frac{3}{17\text{x}19}+\frac{3}{19\text{x}21}\)
\(=\frac{3}{2}\text{x}\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+\frac{1}{17}-\frac{1}{19}+\frac{1}{19}-\frac{1}{21}\right)\)
\(=\frac{3}{2}\text{x}\left(\frac{1}{11}-\frac{1}{21}\right)\)
\(=\frac{3}{2}\text{x}\frac{10}{231}\)
\(=\frac{5}{77}\)