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(\(\dfrac{11}{12}\) + \(\dfrac{11}{12.23}\) + \(\dfrac{11}{23.24}\) + ... + \(\dfrac{11}{89.100}\)) + \(x\) = \(\dfrac{5}{3}\)
Em xem lại nhé chứ \(\dfrac{11}{23.24}\) không hợp quy luật dãy số.
\(\frac{12}{7}\times\frac{2}{11}+\frac{12}{11}\times\frac{15}{7}-\frac{12}{7}\times\frac{6}{11}\)
\(=\frac{12}{7}\times\frac{2}{11}+\frac{12}{7}\times\frac{15}{11}-\frac{12}{7}\times\frac{6}{11}\)
\(=\frac{12}{7}\times\left(\frac{2}{11}+\frac{15}{11}-\frac{6}{11}\right)\)
\(=\frac{12}{7}\times1=\frac{12}{7}\)
\(\frac{12}{7}.\frac{2}{11}+\frac{12}{11}.\frac{15}{7}-\frac{12}{7}.\frac{6}{11}\)
= \(\frac{24}{77}\)+\(\frac{180}{77}\)-\(\frac{72}{77}\)
=\(\frac{132}{77}\)
a) \(\left(\frac{11}{12}+\frac{11}{12.23}+\frac{11}{23.34}+...+\frac{11}{89.100}\right)-x=\frac{2}{3}\)
\(\left(1-\frac{1}{12}+\frac{1}{12}-\frac{1}{23}+\frac{1}{23}-\frac{1}{34}+...+\frac{1}{89}-\frac{1}{100}\right)-x=\frac{2}{3}\)
\(\left(1-\frac{1}{100}\right)-x=\frac{2}{3}\)
\(\frac{99}{100}-x=\frac{2}{3}\)
\(x=\frac{99}{100}-\frac{2}{3}\)
\(x=\frac{97}{300}\)
b) \(\frac{x+1}{9}+\frac{x+3}{7}+\frac{x+5}{5}+\frac{x+7}{3}=a\)
\(\Rightarrow\frac{x+1}{9}+1+\frac{x+3}{7}+1+\frac{x+5}{5}+1+\frac{x+7}{3}+1=a+4\)
\(\frac{x+10}{9}+\frac{x+10}{7}+\frac{x+10}{5}+\frac{x+10}{3}=a+4\)
\(\left(x+10\right).\left(\frac{1}{9}+\frac{1}{7}+\frac{1}{5}+\frac{1}{3}\right)=a+4\)
\(a,\left(\frac{11}{12}+\frac{11}{12\cdot23}+\frac{11}{23\cdot34}+...+\frac{11}{89\cdot100}\right)-x=\frac{2}{3}\)
\(\Rightarrow\left(1-\frac{1}{12}+\frac{1}{12}-\frac{1}{23}+\frac{1}{23}-\frac{1}{34}+...+\frac{1}{89}-\frac{1}{100}\right)-x=\frac{2}{3}\)
\(\Rightarrow1-\frac{1}{100}-x=\frac{2}{3}\)
\(\Rightarrow\frac{99}{100}-x=\frac{2}{3}\)
\(\Rightarrow x=\frac{99}{100}-\frac{2}{3}\)
\(\Rightarrow x=\frac{97}{300}\)
b, k hiểu đề :v
Bài 1:
<=>7[3(-x)]-12(x-5)=-3(11x-20)
=>-3(11x-20)=5
=>-33x=-55
=>-11.3x=-11.5 (rút gọn -11)
=>3x=5
\(\Rightarrow x=\frac{5}{3}\)
Đã duyệt
bài 1:
<=>7[3(-x)]-12(x-5)=-3(11x-20)
=>-3(11x-20)=5
=>-33x=-55
=>-11.3x=-11.5 (rút gọn -11)
=>3x=5
=>x=\(\frac{5}{3}\)
\(\Rightarrow\frac{12-1}{12.1}+\frac{23-12}{12.23}+...+\frac{100-89}{89.100}+x=\frac{2}{3}\)
\(\Rightarrow\frac{12}{12.1}-\frac{1}{12.1}+\frac{23}{12.23}-\frac{12}{12.23}+...+\frac{100}{89.100}-\frac{89}{89.100}+x=\frac{2}{3}\)
Giản ước tử số cho mẫu số ta được:
\(1-\frac{1}{12}+\frac{1}{12}-\frac{1}{23}+...+\frac{1}{89}-\frac{1}{100}+x=\frac{2}{3}\)
\(\Rightarrow1-\frac{1}{100}+x=\frac{2}{3}\)
\(\Rightarrow\frac{99}{100}+x=\frac{2}{3}\)
\(\Rightarrow x=\frac{2}{3}-\frac{99}{100}\)
\(\Rightarrow x=\frac{-97}{300}\)
mình cũng tính cái bài này rồi thế mà ko ra kq