Question

Tìm x, y, z biết:

(2x-1)^2010+(y-2/5)^2010+|x+y-z|=0

Answer 1

Vì \(\hept{\begin{cases}\left(2x-1\right)^{2010}\ge0\\\left(y-\frac{2}{5}\right)^{2010}\ge0\\\left|x+y-z\right|\ge0\end{cases}\forall x,y,z}\)

\(\Rightarrow\left(2x-1\right)^{2010}+\left(y-\frac{2}{5}\right)^{2010}+\left|x+y-z\right|\ge0\)

Mà \(\left(2x-1\right)^{2010}+\left(y-\frac{2}{5}\right)^{2010}+\left|x+y-z\right|=0\)

\(\Leftrightarrow\hept{\begin{cases}\left(2x-1\right)^{2010}=0\\\left(y-\frac{2}{5}\right)^{2010}=0\\\left|x+y-z\right|=0\end{cases}\Leftrightarrow\hept{\begin{cases}2x-1=0\\y-\frac{2}{5}=0\\x+y-z=0\end{cases}\Leftrightarrow}\hept{\begin{cases}x=\frac{1}{2}\\y=\frac{2}{5}\\z=\frac{9}{10}\end{cases}}}\)

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