Tìm x biết :
\(\dfrac{X}{2x5}+\dfrac{X}{5x8}+\dfrac{X}{8x11}+\dfrac{X}{11x14}+...+\dfrac{X}{32x35}=\dfrac{33}{70}\)
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Những câu hỏi liên quan
T
16 tháng 10 2023
\(\dfrac{x}{2\times5}+\dfrac{x}{5\times8}+\dfrac{x}{8\times11}+\dfrac{x}{11\times14}+...+\dfrac{x}{32\times35}=\dfrac{33}{70}\)
\(\dfrac{x}{3}\cdot\left(\dfrac{3}{2\times5}+\dfrac{3}{5\times8}+\dfrac{3}{8\times11}+\dfrac{3}{11\times14}+...+\dfrac{3}{32\times35}\right)=\dfrac{33}{70}\)
\(\dfrac{x}{3}\cdot\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}+...+\dfrac{1}{32}-\dfrac{1}{35}\right)=\dfrac{33}{70}\)
\(\dfrac{x}{3}\cdot\left(\dfrac{1}{2}-\dfrac{1}{35}\right)=\dfrac{33}{70}\)
\(\dfrac{x}{3}\cdot\dfrac{33}{70}=\dfrac{33}{70}\)
\(\dfrac{x}{3}=\dfrac{33}{70}:\dfrac{33}{70}\)
\(\dfrac{x}{3}=1\)
\(x=3\)
VT
28 tháng 3 2022
A = \(\dfrac{1}{2}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{8}\) + \(\dfrac{1}{8}\) - \(\dfrac{1}{11}\) + \(\dfrac{1}{11}\) - \(\dfrac{1}{14}\) + \(\dfrac{1}{14}\) - \(\dfrac{1}{17}\) + \(\dfrac{1}{17}\) - \(\dfrac{1}{20}\)
= \(\dfrac{1}{2}\) - \(\dfrac{1}{20}\)
= \(\dfrac{9}{20}\)
7 tháng 10 2021
\(A=\dfrac{3}{5\cdot8}+\dfrac{3}{8\cdot11}+\dfrac{3}{11\cdot14}+...+\dfrac{3}{100\cdot103}\)
\(=\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{100}-\dfrac{1}{103}\)
\(=\dfrac{98}{515}\)
19 tháng 2 2022
\(x+\dfrac{1}{2}=\dfrac{33}{4}\\ \Rightarrow x=\dfrac{33}{4}-\dfrac{1}{2}\\ \Rightarrow x=\dfrac{31}{4}\\ \dfrac{5}{6}-x=\dfrac{1}{3}\\ \Rightarrow x=\dfrac{5}{6}-\dfrac{1}{3}\\ \Rightarrow x=\dfrac{1}{2}\\ x+\dfrac{4}{5}=\dfrac{-2}{3}\\ \Rightarrow x=\dfrac{-2}{3}-\dfrac{4}{5}\\ \Rightarrow x=\dfrac{-22}{15}\)
28 tháng 8 2023
\(\dfrac{3}{1\times4}x+\dfrac{3}{4\times7}x+\dfrac{3}{7\times10}x+...+\dfrac{3}{31\times34}x=33\)
\(x\left(\dfrac{3}{1\times4}+\dfrac{3}{4\times7}+\dfrac{3}{7\times10}+...+\dfrac{3}{31\times34}\right)=33\)
\(x\left(\dfrac{1}{1}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{31}-\dfrac{1}{34}\right)=33\)
\(x\left(1-\dfrac{1}{34}\right)=33\)
\(\dfrac{33}{34}x=33\)
\(x=34\)
VN
Võ Ngọc Phương
CTVHS
VIP
28 tháng 8 2023
\(\dfrac{3}{1.4}x+\dfrac{3}{4.7}x+\dfrac{3}{7.10}x+...+\dfrac{3}{31.34}x=33\)
\(x.3\left(\dfrac{1}{1.4}+\dfrac{1}{4.7}+\dfrac{1}{7.10}+...+\dfrac{1}{31.34}\right)=33\)
\(x.3.\dfrac{1}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{31}-\dfrac{1}{34}\right)=33\)
\(x.\left(1-\dfrac{1}{34}\right)=33\)
\(x.\dfrac{33}{34}=33\)
\(x=33:\dfrac{33}{34}=33.\dfrac{34}{33}\)
\(x=34\)
NN
1
14 tháng 10 2021
Áp dụng t/c dtsbn:
\(\dfrac{x}{33}=\dfrac{y}{4}=\dfrac{z}{5}=\dfrac{z-x}{5-33}=\dfrac{-196}{-28}=7\)
\(\Rightarrow\left\{{}\begin{matrix}x=7.33=231\\y=7.4=28\\z=7.5=35\end{matrix}\right.\)
TM
16 tháng 3 2021
\(\left(\dfrac{103}{8}-\dfrac{193}{18}\right):x-\dfrac{40}{33}:\dfrac{8}{11}=\dfrac{5}{3}\)
\(\dfrac{155}{72}:x-\dfrac{5}{3}=\dfrac{5}{3}\)
\(\dfrac{155}{72}:x=\dfrac{5}{3}+\dfrac{5}{3}=\dfrac{10}{3}\)
\(x=\dfrac{155}{72}:\dfrac{10}{3}=\dfrac{31}{48}\)
vaayj.....
NT
1
14 tháng 10 2021
\(A=\dfrac{3}{5\times8}+\dfrac{3}{8\times11}+...+\dfrac{3}{2009\times2012}\)
\(A=\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{2009}-\dfrac{1}{2012}\)
\(=\dfrac{1}{5}-\dfrac{1}{2012}=\dfrac{2007}{10060}\)
7 tháng 1
1: Ta có: \(\dfrac{x}{3}=\dfrac{y}{6}\)
mà 4x-y=42
nên Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:
\(\dfrac{x}{3}=\dfrac{y}{6}=\dfrac{4x-y}{4\cdot3-6}=\dfrac{42}{12-6}=\dfrac{42}{6}=7\)
=>\(x=7\cdot3=21;y=6\cdot7=42\)
2: \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{5}\)
mà x-2y+3z=33
nên Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:
\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{5}=\dfrac{x-2y+3z}{2-2\cdot3+3\cdot5}=\dfrac{33}{2-6+15}=\dfrac{33}{11}=3\)
=>\(x=3\cdot2=6;y=3\cdot3=9;z=3\cdot5=15\)
3: \(\dfrac{x}{y}=\dfrac{6}{5}\)
=>\(\dfrac{x}{6}=\dfrac{y}{5}\)
mà x+y=121
nên Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:
\(\dfrac{x}{6}=\dfrac{y}{5}=\dfrac{x+y}{6+5}=\dfrac{121}{11}=11\)
=>\(x=11\cdot6=66;y=11\cdot5=55\)
\(\Leftrightarrow x\cdot\dfrac{1}{3}\cdot\left(\dfrac{3}{2\cdot5}+\dfrac{3}{5\cdot8}+...+\dfrac{3}{32\cdot35}\right)=\dfrac{33}{70}\)
=>\(x\cdot\dfrac{1}{3}\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+...+\dfrac{1}{32}-\dfrac{1}{35}\right)=\dfrac{33}{70}\)
=>\(x\cdot\dfrac{1}{3}\cdot\dfrac{33}{70}=\dfrac{33}{70}\)
=>x=3
Mk bt kết quả là x =1 nhung ko bt cách trình bày