Question

Tìm x, y là STN biết: 25 - y² = 8( x - 2009 ) ^ 2

Answer 1

\(25-y^2=8\left(x-2009\right)^2\)

\(\Leftrightarrow8\left(x-2009\right)^2=25-y^2\)

\(\Leftrightarrow8\left(x-2009\right)^2+y^2=25\)\(\left(1\right)\)

Vì \(y^2\ge0\) nên \(\left(x-2009\right)^2\le\dfrac{25}{8}\)

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

+) Với \(\left(x-2009\right)^2=0\) thay vào \(\left(1\right)\Leftrightarrow y^2=25\Leftrightarrow\left[{}\begin{matrix}y=5\\y=-5\end{matrix}\right.\)

+) Với \(\left(x-2009\right)^2=1\) thay vào \(\left(1\right)\Leftrightarrow y^2=17\) (loại)

Vậy \(\left(x;y\right)=\left(2009;5\right),\left(2009;-5\right)\)