Question

[Cathy Trang]

Tìm x,y,z biết:

(x-2014)¹⁰+(y-2015)¹⁰⁰+(z-2016)¹⁰⁰⁰=0

Answer 1

[Trần Việt Linh]

Vì: \(\left(x-2014\right)^{10}\ge0,\forall x\)

\(\left(y-2015\right)^{100}\ge0,\forall y\)

\(\left(z-2016\right)^{1000}\ge0,\forall z\)

Mà: \(\left(x-2014\right)^{10}+\left(y-2015\right)^{100}+\left(z-2016\right)^{1000}=0\)

\(\Rightarrow\left\{\begin{matrix}x-2014=0\\y-2015=0\\z-2016=0\end{matrix}\right.\)\(\Rightarrow\left\{\begin{matrix}x=2014\\y=2015\\z=2016\end{matrix}\right.\)