Question

Tìm x , y thuộc N biết : 25 - y² = 8 ( x -2009 )²

Answer 1

Ta có \(25-y^2\le25\)

\(\Rightarrow8\left(x-2009\right)\le25\)

\(\Rightarrow\left(x-2009\right)^2\le3\)

\(\Rightarrow\left[\begin{matrix}\left(x-2009\right)^2=0\\\left(x-2009\right)^2=1\end{matrix}\right.\)

\(\left[\begin{matrix}x-2009=0\\\left[\begin{matrix}x-2009=1\\x-2009=-1\end{matrix}\right.\end{matrix}\right.\Rightarrow\left[\begin{matrix}x=2009\\\left[\begin{matrix}x=2010\\x=2008\end{matrix}\right.\end{matrix}\right.\)

Vậy x=2008 hoặc x=2009 hoặc x=2010