Question

( x - 5 )\(^{10}\) + | y\(^2\) - 9 | = 0

Answer 1

Với mọi x, y ta có :

\(\left\{{}\begin{matrix}\left(x-5\right)^{10}\ge0\\\left|y^2-9\right|\ge0\end{matrix}\right.\)

\(\Leftrightarrow\left(x-5\right)^{10}+\left|y^2-9\right|\ge0\)

Mà \(\left(x-5\right)^{10}+\left|y^2-9\right|=0\)

Dấu "=" xảy ra khi :

\(\Leftrightarrow\left\{{}\begin{matrix}\left(x-5\right)^{10}=0\\\left|y^2-9\right|=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-5=0\\y^2-9=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=5\\\left[{}\begin{matrix}y=3\\y=-3\end{matrix}\right.\end{matrix}\right.\)

Vậy..