Đáp án:
Ta có: `(x-1/5)^(2004)>=0 ∀x`
`(y+0,4)^(100)>=0 ∀y`
`(z-3)^(678)>=0 ∀z`
`=> (x-1/5)^(2004)+(y+0,4)^(100)+(z-3)^(678)>=0 ∀x,y,z`
Dấu "=" xảy ra `<=>`
$\left\{\begin{matrix}(x-\dfrac{1}{5})^{2004}=0& \\(y+0,4)^{100}=0&\\ (z-3)^{678}=0& \end{matrix}\right.$
`=>` $\left\{\begin{matrix}x-\dfrac{1}{5}=0& \\y+0,4=0&\\ z-3=0& \end{matrix}\right.$
`=>` $\left\{\begin{matrix}x=\dfrac{1}{5}& \\y=-0,4\\ z=3& \end{matrix}\right.$