tìm các số nguyên x,y biết
\(\dfrac{6}{2x+1}=\dfrac{2}{7}\)
\(\dfrac{24}{7x-3}=\dfrac{-4}{25}\)
\(\dfrac{4}{x-6}=\dfrac{y}{24}=\dfrac{-12}{18}\)
\(\dfrac{-1}{5}\le\dfrac{x}{8}\le\dfrac{1}{4}\)
\(\dfrac{x+46}{20}=x\dfrac{2}{5}\)
\(y\dfrac{5}{y}=\dfrac{56}{y}\) \(\left(x\dfrac{2}{5};y\dfrac{5}{y}\right)\) là các hỗn số
\(\dfrac{6}{2x+1}=\dfrac{2}{7}\)
=> 2(2x+1) = 6.7
4x+2=42
4x=40
x=10
Vậy x=10
a)\(\dfrac{6}{2x+1}=\dfrac{2}{7}\\ =>6.7=2.\left(2x+1\right)\\ =>2x+1=\dfrac{6.7}{2}=\dfrac{42}{2}=21\\ =>2x=21-1=20\\ =>x=\dfrac{20}{2}=10\)
b) \(\dfrac{24}{7x-3}=-\dfrac{4}{25}\\ =>24.25=-4.\left(7x-3\right)\\ =>7x-3=\dfrac{24.25}{-4}=-150\\ =>7x=-150+3=-147\\ =>x=\dfrac{-147}{7}=-21\)
c) \(\dfrac{4}{x-6}=\dfrac{y}{24}=-\dfrac{12}{18}\\ =>x-6=\dfrac{4.18}{-12}=-6\\ =>x=-6+6=0\\ y=\dfrac{-12.24}{18}=-16\)
d) \(-\dfrac{1}{5}\le\dfrac{x}{8}\le\dfrac{1}{4}\\ < =>-\dfrac{8}{40}\le-\dfrac{5x}{40}\le\dfrac{10}{40}\\ =>-8\le-5x\le10\\ Mà:-8< -5.1< -5.0< -5.\left(-1\right)< -5.\left(-2\right)=10\\ =>x\in\left\{-2;-1;0;1\right\}\)
e) \(\dfrac{x+46}{20}=x\dfrac{2}{5}\\ < =>\dfrac{x+46}{20}=\dfrac{5x+2}{5}\\ =>5\left(x+46\right)=20\left(5x+2\right)\\ < =>5x+230=100x+40\\ < =>230-40=100x-5x\\ < =>190=95x\\ =>x=\dfrac{190}{95}=2\)
f) \(y\dfrac{5}{y}=\dfrac{56}{y}\\ < =>\dfrac{y^2+5}{y}=\dfrac{56}{y}\\ =>y\left(y^2+5\right)=56y\\ =>y^2+5=\dfrac{56y}{y}=56\\ =>y^2=56-5=51\\ =>y=\sqrt{51}\)
\(\dfrac{24}{7x-3}=\dfrac{-4}{25}\)
\(\Rightarrow\left(7x-3\right).\left(-4\right)=24.25\)
\(\Rightarrow-28x+12=600\)
\(\Rightarrow-28x=600-12=588\)
\(\Rightarrow\)\(x=588:\left(-28\right)=-21\)
Vậy \(x=-21\)
\(a\)) \(\dfrac{6}{2x+1}=\dfrac{2}{7}\)
\(\Leftrightarrow2\left(2x+1\right)=6\cdot7\)
\(\Leftrightarrow4x+2=42\)
\(\Leftrightarrow4x=40\)
\(\Leftrightarrow x=10\)
Vậy \(x=10\)
\(b\)) \(\dfrac{24}{7x-3}=\dfrac{-4}{25}\)
\(\Leftrightarrow-4\left(7x-3\right)=24\cdot25\)
\(\Leftrightarrow-4\left(7x-3\right)=600\)
\(\Leftrightarrow7x-3=-150\)
\(\Leftrightarrow7x=-147\)
\(\Leftrightarrow x=-21\)
Vậy \(x=-21\)
\(c\)) \(\dfrac{4}{x-6}=\dfrac{y}{24}=\dfrac{-12}{18}\)
Ta có: \(\dfrac{4}{x-6}=\dfrac{-12}{18}\)
\(\Leftrightarrow-12\left(x-6\right)=72\)
\(\Leftrightarrow x-6=-6\)
\(\Leftrightarrow x=0\)
\(\dfrac{y}{24}=\dfrac{4}{x-6}\)
\(\Leftrightarrow\dfrac{y}{24}=\dfrac{-2}{3}\)
\(\Leftrightarrow y=\dfrac{-2}{3}\cdot24\)
\(\Leftrightarrow y=-16\)
Vậy \(x=0\)
\(y=-16\)
\(d\)) \(-\dfrac{1}{5}\le\dfrac{x}{8}\le\dfrac{1}{4}\)
\(\Leftrightarrow-0,2\le x\le0,25\)\(\)
Mà \(x\in Z\)
\(\Leftrightarrow x=0\)
Vậy \(x=0\)
\(e\)) \(\dfrac{x+46}{20}=x\dfrac{2}{5}\)
\(\Leftrightarrow\dfrac{x+46}{20}=\dfrac{5x+2}{5}\)
\(\Leftrightarrow5\left(x+46\right)=20\left(5x+2\right)\)
\(\Leftrightarrow5x+230=100x+40\)
\(\Leftrightarrow5x-100x=40-230\)
\(\Leftrightarrow-95x=-190\)
\(\Leftrightarrow x=\dfrac{-190}{-95}\)
\(\Leftrightarrow x=2\)
Vậy \(x=2\)
\(f\)) \(y\dfrac{5}{y}=\dfrac{56}{y}\)
\(\Leftrightarrow\dfrac{y^2+5}{y}=\dfrac{56}{y}\)
\(\Leftrightarrow\left(y^2+5\right)y=56y\)
\(\Leftrightarrow y^3+5y=56y\)
\(\Leftrightarrow y^3=56y-5y\)
\(\Leftrightarrow y^3=51y\)
\(\Leftrightarrow\dfrac{y^3}{y}=51\)
\(\Leftrightarrow y^2=51\)
\(\Leftrightarrow y=\sqrt{51}\)
\(\Leftrightarrow y=7,141...\)
Mà \(y\in Z\)
Vậy \(y\) không có giá trị
a, \(\dfrac{6}{2x+1}=\dfrac{2}{7}\)
\(\Rightarrow2\left(2x+1\right)=6.7\)
\(\Rightarrow4x+2=42\)
\(\Rightarrow4x=40\)
\(\Rightarrow x=10\)
b, \(\dfrac{24}{7x-3}=\dfrac{-4}{25}\)
\(\Rightarrow-4\left(7x-3\right)=24.25\)
\(\Rightarrow-28x+12=600\)
\(\Rightarrow-28x=588\)
\(\Rightarrow x=-21\)
c, \(\dfrac{4}{x-6}=\dfrac{y}{24}=\dfrac{-12}{18}\)
\(\dfrac{4x}{x-6}=\dfrac{-12}{18}\)
\(\Rightarrow\dfrac{4x}{x-6}=\dfrac{-2}{3}\)
\(\Rightarrow12x=-2\left(x-6\right)\)
\(\Rightarrow12x=-2x+12\)
\(\Rightarrow12x+2x=12\)
\(\Rightarrow14x=12\)
\(\Rightarrow x=\dfrac{6}{7}\)
