Question

Cho (3x-5)^2018 + (y^2 - 1)^2006 + (x-z)^2100 = 0

Tìm x , y , z

Answer 1

\(\left(3x-5\right)^{2018}+\left(y^2-1\right)^{2006}+\left(x-z\right)^{2100}=0\)

ta có \(\left\{{}\begin{matrix}\left(x-z\right)^{2100}\ge0\\\left(y^2-1\right)^{2006}\ge0\\\left(3x-5\right)^{2018}\ge0\end{matrix}\right.\)

dấu = xảy ra khi \(\left\{{}\begin{matrix}3x-5=0\\y^2-1=0\\z-x=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5}{3}\\z=x\\\left[{}\begin{matrix}y=1\\y=-1\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=\dfrac{5}{3}\\y=1\\z=\dfrac{5}{3}\end{matrix}\right.\\\left\{{}\begin{matrix}x=\dfrac{5}{3}\\y=-1\\z=\dfrac{5}{3}\end{matrix}\right.\end{matrix}\right.\)

vậy.................