Question

Tìm x,y,z biết

( 2x-1)²⁰¹⁶  + ( y - \(\frac{2}{5}\) )²⁰¹⁶ + I x + y - z I = 0

Answer 1

Do \(\left(2x-1\right)^{2016}\ge0;\left(y-\frac{2}{5}\right)^{2016}\ge0;\left|x+y-z\right|\ge0\)

Mà theo đề bài: \(\left(2x-1\right)^{2016}+\left(y-\frac{2}{5}\right)^{2016}+\left|x+y-z\right|=0\)

=> \(\begin{cases}\left(2x-1\right)^{2016}=0\\\left(y-\frac{2}{5}\right)^{2016}=0\\\left|x+y-z\right|=0\end{cases}\)=> \(\begin{cases}2x-1=0\\y-\frac{2}{5}=0\\x+y-z=0\end{cases}\)=> \(\begin{cases}2x=1\\y=\frac{2}{5}\\x+y=z\end{cases}\)=> \(\begin{cases}x=\frac{1}{2}\\y=\frac{2}{5}\\x+y=z\end{cases}\)

=> \(\begin{cases}x=\frac{1}{2}\\y=\frac{2}{5}\\z=\frac{9}{10}\end{cases}\)

Vậy \(x=\frac{1}{2};y=\frac{2}{5};z=\frac{9}{10}\)