Question

Tìm x , y biết :

| x² - 4 | + ( y² - 25 )² = 0

Answer 1

Với mọi x,y ta có :

\(\left\{{}\begin{matrix}\left|x^2-4\right|\ge0\\\left(y^2-25\right)^2\ge0\end{matrix}\right.\)

Mà \(\left|x^2-4\right|+\left(y^2-25\right)^2=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left|x^2-4\right|=0\\\left(y^2-25\right)^2=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x^2-4=0\\y^2-25=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\\\left[{}\begin{matrix}y=5\\y=-5\end{matrix}\right.\end{matrix}\right.\)

Vậy..