Question

[Trèo lên cột điện thế hiện tình yêu]

\(\left(2x-5\right)^{2000}+\left(3y+4\right)^{2002}\le0\)

Tìm X,Y

Answer 1

[Nguyễn Thanh Hằng]

\(\left(2x-5\right)^{2000}+\left(3y+4\right)^{2002}\le0\)\(\left(1\right)\)

Mà \(\left\{{}\begin{matrix}\left(2x-5\right)^{2000}\ge0\\\left(3y+4\right)^{2002}\ge0\end{matrix}\right.\)

\(\Leftrightarrow\left(2x-5\right)^{2000}+\left(3y+4\right)^{2002}\ge0\left(2\right)\)

Từ \(\left(1\right)+\left(2\right)\Leftrightarrow\left(2x-5\right)^{2000}+\left(3y+4\right)^{2002}=0\)

Mà \(\left\{{}\begin{matrix}\left(2x-5\right)^{2000}\ge0\\\left(3y+4\right)^{2002}\ge0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(2x-5\right)^{2000}=0\\\left(3y+4\right)^{2002}=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x-5=0\\3y+4=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5}{2}\\y=-\dfrac{4}{3}\end{matrix}\right.\)

Vậy ..

Answer 2

[Hebico may mắn]

Ta có : \(\left\{{}\begin{matrix}\left(2x-5\right)^{2000}\ge0\\\left(3y+4\right)^{2002}\ge0\end{matrix}\right.\)

Mà \(\left(2x-5\right)^{2000}+\left(3y+4\right)^{2002}\le0\)

\(\Rightarrow\left(2x-5\right)^{2000}+\left(3y+4\right)^{2002}=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x-5=0\\3y+4=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}2x=5\\3y=-4\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5}{2}\\y=-\dfrac{4}{3}\end{matrix}\right.\)

Vậy \(x=\dfrac{5}{2}\) \(;y=-\dfrac{4}{3}\)