Question

[Nguyễn Huế]

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

Answer 1

[NGUYỄN CẨM TÚ]

\(\dfrac{6}{2x+1}=\dfrac{2}{7}\)

=> 2(2x+1) = 6.7

4x+2=42

4x=40

x=10

Vậy x=10

Answer 2

[Nguyễn Trần Thành Đạt]

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) \(y\dfrac{5}{y}=\dfrac{56}{y}\\ < =>\dfrac{y^2+5}{y}=\dfrac{56}{y}\\ =>y\left(y^2+5\right)=56y\\ =>y^2+5=\dfrac{56y}{y}=56\\ =>y^2=56-5=51\\ =>y=\sqrt{51}\)