\(\Leftrightarrow\left|\left(x-y+1\right)^2+x-2\right|=2x-\left|\left(x-1\right)\left(x-2\right)\right|\)
Có \(\left|\left(x-2\right)\left(x-1\right)\right|\ge0\Rightarrow\left[{}\begin{matrix}x\le1\left(1\right)\\x\ge2\left(2\right)\end{matrix}\right.\)-Trường hợp (1) có PT:
\(x-2\ge0\Rightarrow\left(x-y+1\right)^2+x-2>0\)..PT trở thành
\(\left(x-y+1\right)^2+x-2+4=2x-\left(x^2-3x+2\right)\)
\(\Leftrightarrow2x^2-2xy+y^2-4x-2y+5=0\)
Giải nữa thì nhờ mk nha
Với \(x\ge2\)
\(\Rightarrow x-2\ge0\).PT trở thành :
\(x^2-2xy+y^2+3x-2y-1+4=2x-\left(x^2-3x+2\right)\)
\(\Leftrightarrow2x^2-2xy+y^2-2x-2y+5=0\)
\(\Leftrightarrow\left(x^2-2xy+y^2+2x-2y+1\right)+\left(x^2-4x+4\right)=0\)
\(\Leftrightarrow\left(x-y+1\right)^2+\left(x-2\right)^2=0\Rightarrow\left[{}\begin{matrix}x=y-1\\x=2\Rightarrow y=3\end{matrix}\right.\)
Với x\(\le1\).Trị tuyệt đối VT ko thể phá nên xét 2 trường hợp
PT\(\Leftrightarrow|x^2-2xy+y^2+3x-2y-1|=2x-\left(x^2-3x+2\right)-4\)
\(\Leftrightarrow...=-x^2+7x-6.VT\ge0\Rightarrow VP\ge0\Leftrightarrow x^2-7x+6\le0\Leftrightarrow\left(x-1\right)\left(x-6\right)\le0\Rightarrow\left[{}\begin{matrix}x\le1\\x\le6\end{matrix}\right.\)
Có \(\left\{{}\begin{matrix}x^2-2xy+y^2+3x-2y+3=x^2-7x+6\\x^2-2xy+y^2+3x-2y+3=-x^2+7x-6\left(đãCM\right)\end{matrix}\right.\)
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