Question

Giải pt:\(y^2-2y+3=\dfrac{6}{x^2+2x+4}\)

Answer 1

Ta có \(y^2-2y+3=y^2-2y+1+2=\left(y-1\right)^2+2\ge2\)

\(\dfrac{6}{x^2+2x+4}=\dfrac{6}{x^2+2x+1+3}=\dfrac{6}{\left(x+1\right)^2+3}\le2\)

Vậy \(y^2-2y+3=\dfrac{6}{x^2+2x+4}=2\Leftrightarrow\)\(\left\{{}\begin{matrix}y^2-2y+3=2\\\dfrac{6}{x^2+2x+4}=2\end{matrix}\right.\)\(\Leftrightarrow\)\(\left\{{}\begin{matrix}\left(y-1\right)^2+2=2\\\dfrac{6}{\left(x+1\right)^2+3}=2\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}y=1\\x=-1\end{matrix}\right.\)

Answer 2

\(y^2-2y+3=\left(y-1\right)^2+2\ge2\)

\(\dfrac{6}{x^2+2x+4}=\dfrac{6}{\left(x+1\right)^2+3}\le2\)

So ez