Question

\(\left(x-\dfrac{1}{2}\right)^{50}+\left(y+\dfrac{1}{3}\right)^{40}=0\)

Answer 1

ta có : \(\left(x-\dfrac{1}{2}\right)^{50}\ge0\) với mọi \(x\) và \(\left(y+\dfrac{1}{3}\right)^{40}\ge0\) vơi mọi \(y\)

\(\Rightarrow\left(x-\dfrac{1}{2}\right)^{50}+\left(y+\dfrac{1}{3}\right)^{40}\ge0\) với mọi \(x;y\)

\(\Rightarrow\left(x-\dfrac{1}{2}\right)^{50}+\left(y+\dfrac{1}{3}\right)^{40}=0\) \(\Leftrightarrow\left[{}\begin{matrix}\left(x-\dfrac{1}{2}\right)^{50}=0\\\left(y+\dfrac{1}{3}\right)^{40}=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{1}{2}=0\\y+\dfrac{1}{3}=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\y=\dfrac{-1}{3}\end{matrix}\right.\) vậy \(x=\dfrac{1}{2};y=\dfrac{-1}{3}\)