Question

tìm x,y,z biết(2x-1)^2022+(y-2/5)^2022+|x+y-z|=0

Answer 1

\(\left(2x-1\right)^{2020}+\left(y-\frac{2}{5}\right)^{2022}+\left|x+y-z\right|=0\)

Ta có : \(\left(2x-1\right)^{2020}\ge0\forall x;\left(y-\frac{2}{5}\right)^{2022}\ge0\forall x;\left|x+y-z\right|\ge0\forall x;y;z\)

Dấu bằng xảy ra <=> \(x=\frac{1}{2};y=\frac{2}{5};z=x+y=\frac{1}{2}+\frac{2}{5}=\frac{9}{10}\)

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