Question

Tìm x , y thuộc  Z biết

  xy - 2x = 5

Answer 1

xy - 2x       = 5

x . ( y - 2 ) = 5

=> x và ( y - 2 ) ∈ Ư(5)

Mà Ư(5) = { 1 ; 5 ; - 1 ; - 5 }

TH1: x = 1 ; ( y - 2 ) = 5

y - 2 = 5

y      = 5 + 2

y      = 7

TH2: x = 5 ; ( y - 2 ) = 1

y - 2 = 1

y      = 1 + 2

y      = 3

TH3: x = - 1 ; ( y - 2 ) = - 5

y - 2 = - 5

y      = - 5 + 2

y      = - 3

TH4: x = - 5 ; ( y - 2 ) = - 1

y - 2 = - 1 

y      = - 1 + 2

y      =  1 
Vậy x ∈ { 1 ; 5 ; - 1 ; - 5 }

       y ∈ { 7 ; 3 ; - 3 ; 1 }  

Answer 2

\(\text{xy - 2x = 5}\)

\(\text{x . ( y - 2 ) = 5}\)

\(\Rightarrow x.\left(y-2\right)=5.1=1.5=\left(-1\right).\left(-5\right)=\left(-5\right).\left(-1\right)\)

x	5	1	-1	-5
y - 2	1	5	-5	-1
y	3	7	-3	1

\(\left(x,y\right)\in\left\{\left(5;3\right),\left(1;7\right),\left(-1;-3\right),\left(-5;1\right)\right\}\)

Answer 3

\(xy-2x=5\Leftrightarrow x\left(y-2\right)=5\)

Do vế phải dương nên x và y - 2 đồng dấu

Ta có bảng: 

x	5	1	-1	-5
y -2	1	5	-5	-1
y	3	7	-3	1

Vậy (x;y) = (5;3) ; (1;7) ; (-1;-3) ; (-5;1)

Answer 4

\(xy-2x=5\)

\(\Rightarrow x\left(y-2\right)=5\)

\(\Rightarrow x,\left(y-2\right)\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\)

\(\Rightarrow TH1:\hept{\begin{cases}x=1\\y-2=5\end{cases}\Rightarrow\hept{\begin{cases}x=1\\y=7\end{cases}}}\)       \(TH2:\hept{\begin{cases}x=-1\\y-2=-5\end{cases}\Rightarrow\hept{\begin{cases}x=-1\\y=-3\end{cases}}}\)

\(TH3:\hept{\begin{cases}x=5\\y-2=1\end{cases}\Rightarrow\hept{\begin{cases}x=5\\y=3\end{cases}}}\)                 \(TH4:\hept{\begin{cases}x=-5\\y-2=-1\end{cases}\Rightarrow\hept{\begin{cases}x=-5\\y=-1\end{cases}}}\)

Vậy ..............................

Answer 5

\(xy-2x=5\)

\(\Leftrightarrow x\left(y-2\right)=5\)

\(\Leftrightarrow x\inƯ\left(5\right)=\left\{-5;-1;1;5\right\}\)

\(\text{Trường hợp : }x=-5\)

\(\Leftrightarrow-5\left(v-2\right)=5\)

\(\Leftrightarrow y-2=5\div\left(-5\right)\)

\(\Leftrightarrow y-2=-1\)

\(\Leftrightarrow y=-1+2\)

\(\Leftrightarrow y=1\)

\(\text{Trường hợp : }x=-1\)

\(\Leftrightarrow-1\left(y-2\right)=5\)

\(\Leftrightarrow y-2=5\div\left(-1\right)\)

\(\Leftrightarrow y-2=-5\)

\(\Leftrightarrow y=-5+2\)

\(\Leftrightarrow y=-3\)

\(\text{Trường hợp : }x=1\)

\(\Leftrightarrow1\left(y-2\right)=5\)

\(\Leftrightarrow y-2=5\)

\(\Leftrightarrow y=5+2\)

\(\Leftrightarrow y=7\)

\(\text{Trường hợp : }x=5\)

\(\Leftrightarrow5\left(y-2\right)=5\)

\(\Leftrightarrow y-2=1\)

\(\Leftrightarrow y=1+2\)

\(\Leftrightarrow y=3\)

\(\text{Vậy }x,y\in\left\{\left(5,1\right);\left(-1,-3\right);\left(1,7\right);\left(5,3\right)\right\}\)