Question

Tìm các số nguyên x,y sao cho:

a) \(\dfrac{x}{5}\)=\(\dfrac{6}{-10}\) ; b) \(\dfrac{x}{3}=\dfrac{4}{y}\) ; c) \(\dfrac{x}{y}=\dfrac{2}{7}\) ; d) \(\dfrac{2}{x}=\dfrac{x}{8}\)

Answer 1

a) \(\dfrac{x}{5}=\dfrac{6}{-10}\)

\(\Rightarrow\) (-10).x=5.6

\(\Leftrightarrow\) (-10).x=30

\(\Leftrightarrow x=30:\left(-10\right)\)

\(\Leftrightarrow\) x=(-3)

Vậy......................

b) \(\dfrac{x}{3}=\dfrac{4}{y}\)

\(\Rightarrow xy=3.4=12\)

Ta có: xy=12=1.12=12.1=2.6=6.2=3.4=4.3=(-1).(-12)=......( bạn tự ghi nốt)

\(\Rightarrow\)(x;y)=(1;12) (12;1) (2;6) (6;2) (3;4) (4;3) (-1;-12) (-12;-1) (-2;-6) (-6;-2) (-3;-4) (-4;-3)

Vậy.....................................

Answer 2

a: x/5=6/-10

=>x/5=-3/5

=>x=-3

b: =>xy=12

=>\(\left(x,y\right)\in\left\{\left(1;12\right);\left(12;1\right);\left(-1;-12\right);\left(-12;-1\right);\left(2;6\right);\left(6;2\right);\left(-2;-6\right);\left(-6;-2\right);\left(3;4\right);\left(4;3\right);\left(-3;-4\right);\left(-4;-3\right)\right\}\)

c: =>x/2=y/7=k

=>x=2k; y=7k

=>\(\left(x,y\right)\in\left\{\left(2k;7k\right);k\in Z\right\}\)

d: 2/x=x/8

=>x^2=16

=>x=4 hoặc x=-4