\(\text{Ta có:}\dfrac{x}{8}=\dfrac{2}{x}\)

\(\Rightarrow\dfrac{x}{8}.8x=\dfrac{2}{x}.8x\)

\(\Rightarrow x^2=16\)

\(\Rightarrow\left[{}\begin{matrix}x^2=\left(-4\right)^2\\x^2=4^2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-4^{ }\\x^{ }=4^{ }\end{matrix}\right.\)

\(\text{Vậy }x\in\left\{-4;4\right\}\)

\(\dfrac{2}{x}=\dfrac{x}{8}\)

nên \(x^2=16\)

hay \(x\in\left\{4;-4\right\}\)

tìm các số nguyên x , y biết  5\x + 4\y = 1\8 - Hoc24

`C = (x+4)/(x+1) = (x+1+3)/(x+1) = 1+3/(x+1)`

Để `C in ZZ`

`=> x+1 in Ư(3)=(+-1,+-3)`

`@ x+1  =1 => x =0`

`@ x+1=-1 => x = -2`

`@x+1 =3 => x = 2`

`@x+1 =-3 =>x=-4`

`B = (x-4)/(x+2) = (x+2-6)/(x+2) = 1-6/(x+2)`

Để `B in ZZ`

`=> x+2 in Ư(6) = {+-1,+-2,+-3,+-6)`

`@ x+2 =1 => x = -1`

`@x+2 =-1 => x=-3`

`@ x+2 =2 => x=0`

`@ x+2 =-2 => x=-4`

`@x+2 =3 => x = 1`

`@ x +2 =-3 => x = -5`

`@ x+2 =6 => x=4`

`@x+2 =-6 => x= -8`

1<4/x<=-5/8

mà 1>-5/8

nên \(x\in\varnothing\)

a: =>19/23>19/x>19/29

=>\(x\in\left\{24;25;26;27;28\right\}\)

b: =>88/132<88/x<88/128

=>132>x>128

=>\(x\in\left\{131;130;129\right\}\)

c: =>\(\left\{{}\begin{matrix}\dfrac{4}{x}-\dfrac{x}{8}< 0\\\dfrac{x}{8}-\dfrac{5}{x}< 0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{32-x^2}{8x}< 0\\\dfrac{x^2-40}{8x}< 0\end{matrix}\right.\)

=>32<x^2<40

=>x=6

em tham khảo

\(\Rightarrow3xy=12-11y\Leftrightarrow3xy+11y=12\)

\(\Leftrightarrow y\left(3x+11\right)=12\Rightarrow y;3x+11\inƯ\left(12\right)=12\left\{\pm1;\pm2;\pm3;\pm4;\pm6;\pm\right\}\)

-> bạn tự lập bảng 

\(a,=\dfrac{\sqrt{x}-8+5}{\sqrt{x}-8}=1+\dfrac{5}{\sqrt{x}-8}\in Z\\ \Leftrightarrow\sqrt{x}-8\inƯ\left(5\right)=\left\{-5;-1;1;5\right\}\\ \Leftrightarrow\sqrt{x}\in\left\{3;7;9;13\right\}\\ \Leftrightarrow x\in\left\{9;49;81;169\right\}\left(tm\right)\\ b,=\dfrac{\sqrt{x}-2+7}{\sqrt{x}-2}=1+\dfrac{7}{\sqrt{x}-2}\in Z\\ \Leftrightarrow\sqrt{x}-2\inƯ\left(7\right)=\left\{-1;1;7\right\}\left(\sqrt{x}-2>-2\right)\\ \Leftrightarrow\sqrt{x}\in\left\{1;3;9\right\}\\ \Leftrightarrow x\in\left\{1;9;81\right\}\\ c,=\dfrac{2\left(\sqrt{x}+3\right)+2}{\sqrt{x}+3}=2+\dfrac{2}{\sqrt{x}+3}\in Z\\ \Leftrightarrow\sqrt{x}+3\inƯ\left(2\right)=\varnothing\left(\sqrt{x}+3>3\right)\\ \Leftrightarrow x\in\varnothing\)