Question

Tìm số nguyên x,y biết:

a) |x - y -2| + |y + 2| = 0

b) |x - 3y|²⁰⁰⁷ + |y + 4|²⁰⁰⁸ = 0

c) |x - 2003|²⁰⁰³ + |x - 2004|²⁰⁰⁴ = 1

Answer 1

a/ Ta có :

\(\left\{{}\begin{matrix}\left|x-y-2\right|\ge0\\\left|y+2\right|\ge0\end{matrix}\right.\) \(\forall x;y\)

\(\Leftrightarrow\left|x-y-2\right|+\left|Y+2\right|\ge0\)

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

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

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

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

\(\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=2\end{matrix}\right.\)

b/c tương tự