Question

[Nguyễn Hữu Hoàng Hải Anh]

 tìm x và y biết:

 x - 2xy + y = 0

Answer 1

[ngonhuminh]

Lớp 7 giao luu lớp 8 mới máu chứ!!

<=> x(1-2y)+y=0

2x(1-2y)+2y=0

2x(1-2y)+2y-1+1=0

2x(1-2y)-(1-2y)+1=0

(1-2y)(2x-1)+1=0

(2y-1)(2x-1)=1=1.1=(-1).(-1)

2y-1=1&2x-1=1=> y=0; x=0

2y-1=-1&2x-1=-1=> y=1; x=1

Answer 2

[ngonhuminh]

\(giaoluu:\Leftrightarrow x\left(1-2y\right)=-y\Leftrightarrow x=\frac{y}{2y-1}\)

\(!y!\ge!2y-1!\Leftrightarrow y^2\ge4y^2-4y+1\Rightarrow3y^2-4y+1\le0\)

\(\Leftrightarrow\left(y-\frac{2}{3}\right)^2-\frac{1}{9}\le0\Leftrightarrow\left(y-\frac{2}{3}\right)^2\le\left(\frac{1}{3}\right)^2\)

Nghiêm nguyên

\(\Leftrightarrow!\left(y-\frac{2}{3}\right)!\le\frac{1}{3}\hept{\begin{cases}y-\frac{2}{3}\ge-\frac{1}{3}\\y-\frac{2}{3}\le\frac{1}{3}\end{cases}}\Leftrightarrow-\frac{1}{3}\le y\le1\)

=> y={0,1}

x=(0,1)

(x,y)=(0,0); (1,1)