tìm x biết: x-20/11x13-20x13x15-20/15x17-............-20/53x55=3/1
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NN
2
S
18 tháng 5 2017
\(x-\frac{20}{11.13}-\frac{20}{13.15}-\frac{20}{15.17}-...-\frac{20}{53.55}=\frac{3}{11}\)
\(\Rightarrow x-\left(\frac{20}{11.13}+\frac{20}{13.15}+\frac{20}{15.17}+...+\frac{20}{53.55}\right)=\frac{3}{11}\)
Đặt S = \(\frac{20}{11.13}+\frac{20}{13.15}+\frac{20}{15.17}+....+\frac{20}{53.55}\)
\(=10\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{53.55}\right)\)
\(=10\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{53}-\frac{1}{55}\right)\)
\(=10\left(\frac{1}{11}-\frac{1}{55}\right)\)
\(=10\cdot\frac{4}{55}=\frac{8}{11}\)
Thay A vào đề bài,ta được:
\(x-\frac{8}{11}=\frac{3}{11}\)
\(x=\frac{3}{11}+\frac{8}{11}\)
\(x=1\)
10 tháng 7 2017
Bài 3 :
b) Ta có 1+ 2 + 3 +4 + ...+ x =15
Nên \(\frac{x\left(x+1\right)}{2}=15\)
\(x\left(x+1\right)=30\)
=> \(x\left(x+1\right)=5.6\)
=> x = 5
10 tháng 8 2017
Nhân thêm 2
=>(13-11/11x13+...+21-19/19x21)-x+221/231=4/3
=>(13/11x13-11/11x13+...+21/19x21-19/19x21)-x+221/231=4/3
=>(1/11-1/13+...+1/18-1/21)-x+221/231=4/3
=>(1/11-1/21)-x+221/231=4/3
=>10/231-x+221/231=4/3
=>10/231+221/231-x=4/3
=>231/231-x=4/3
=>1-x=4/3
=>x=1-4/3=-1/3
NN
3
8 tháng 2 2017
\(\left(\frac{2}{11x13}+\frac{2}{13x15}+\frac{2}{15x17}+\frac{2}{17x19}+\frac{2}{19x21}\right)\)) x 462 - y = 19
\(=\left(\frac{13-11}{11x13}+\frac{15-13}{13x15}+\frac{17-15}{15x17}+\frac{19-17}{17x19}+\frac{21-19}{19x21}\right)\)x 462 - y = 19
\(=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+\frac{1}{17}-\frac{1}{19}+\frac{1}{19}-\frac{1}{21}\)) x 462 - y = 19
\(=\left(\frac{1}{11}-\frac{1}{21}\right)\)x 462 - y = 19
\(=\left(\frac{21}{231}-\frac{11}{231}\right)\)x 462 - y = 19
\(=\frac{10}{231}\)x 462 - y = 19
\(=20\)- y = 19
y = 20 - 19
y = 1
Ta có :
\(x-\frac{20}{11.13}-\frac{20}{13.15}-\frac{20}{15.17}-...-\frac{20}{53.55}=\frac{3}{1}\)
\(x-\left(\frac{20}{11.13}+\frac{20}{13.15}+\frac{20}{15.17}+...+\frac{20}{53.55}\right)=\frac{3}{1}\)
Đặt \(A=\frac{20}{11.13}+\frac{20}{13.15}+\frac{20}{15.17}+...+\frac{20}{53.55}\)
\(A=10\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{53.55}\right)\)
\(A=10\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{53}-\frac{1}{55}\right)\)
\(A=10\left(\frac{1}{11}-\frac{1}{55}\right)\)
\(A=10.\frac{4}{55}=\frac{40}{55}=\frac{8}{11}\)
\(\Rightarrow x-\frac{8}{11}=\frac{3}{1}=3\)
\(x=3+\frac{8}{11}=\frac{33}{11}+\frac{8}{11}=\frac{41}{11}\)
Ủng hộ mk nha !!! ^_^
><in lỗi bn, 3/11 chứ k phải \(\frac{3}{1}\)