Question

Tìm GTNN của biểu thức: A = |x - 3| + ( y + 2 )⁴ + 2016

Answer 1

Ta thấy: \(\left\{\begin{matrix}\left|x-3\right|\ge0\\\left(y+2\right)^4\ge0\end{matrix}\right.\)

\(\Rightarrow\left|x-3\right|+\left(y+2\right)^4\ge0\)

\(\Rightarrow\left|x-3\right|+\left(y+2\right)^4+2016\ge2016\)

\(\Rightarrow A\ge2016\)

Dấu "=" xảy ra khi \(\left\{\begin{matrix}\left|x-3\right|=0\\\left(y+2\right)^4=0\end{matrix}\right.\)\(\Rightarrow\left\{\begin{matrix}x=3\\y=-2\end{matrix}\right.\)

Vậy \(Min_A=2016\) khi \(\left\{\begin{matrix}x=3\\y=-2\end{matrix}\right.\)