Question

Tìm x;y nguyên khác 0 sao cho:

x + 2y = x.y = x : y

Answer 1

Ta có:

x + 2y = x.y => x = x.y - 2y = y.(x - 2)

=> x : y = x - 2 = x + 2y

=> 2y = -2

=> y = -1

=> x = -1.(x - 2) = -x + 2

=> x + x = 2 = 2x

=> x = 1

Vậy x = 1; y = -1

Answer 2

\(x.y=x:y\)  \(\Rightarrow y^2=1\)  \(\Rightarrow\left[\begin{array}{nghiempt}x=1\\x=-1\end{array}\right.\)

(+) x=1

\(\Rightarrow x+2.1=x.1\)

\(\Rightarrow x+2=x\)

\(\Rightarrow0=-2\) ( vô lý )

(+) Vớ x = - 2

\(\Rightarrow x+2\left(-1\right)=x\left(-1\right)\)

\(\Rightarrow x-3=-x\)

\(\Rightarrow x=\frac{3}{2}\)

Vậy \(\left(x;y\right)=\left(-1;\frac{3}{2}\right)\)