Question

Tìm x biết:

\(\left(3x-5\right)^{2006}+\left(y^2-1\right)^{2008}+\left(x-z\right)^{2100}=0\)

Answer 1

Khó thế? >:(

Answer 2

Ta có: \(\left(3x-5\right)^{2006}\ge0\forall x\)

\(\left(y^2-1\right)^{2008}\ge0\forall y\)

\(\left(x-z\right)^{2010}\ge0\forall x,z\)

Do đó: \(\left(3x-5\right)^{2006}+\left(y^2-1\right)^{2008}+\left(x-z\right)^{2010}>=0\forall x,y,z\)

Dấu '=' xảy ra khi \(\begin{cases}3x-5=0\\ y^2-1=0\\ z-x=0\end{cases}\Rightarrow\begin{cases}3x=5\\ y^2=1\\ z=x\end{cases}\Rightarrow\begin{cases}x=\frac53\\ y\in\left\lbrace1;-1\right\rbrace\\ z=x=\frac53\end{cases}\)