Question

Tìm GTNN

B=(x-1)^2016+\(\left|y+3\right|\) +2017

Answer 1

Có: \(\left(x-1\right)^{2016}\ge0\forall x;\left|y+3\right|\ge0\forall y\)

\(\Rightarrow B=\left(x-1\right)^{2016}+\left|y+3\right|+2017\ge2017\)

Dấu ''='' xảy ra khi \(\begin{cases}\left(x-1\right)^{2016}=0\\\left|y+3\right|=0\end{cases}\)\(\Rightarrow\begin{cases}x-1=0\\y+3=0\end{cases}\)\(\Rightarrow\begin{cases}x=1\\y=-3\end{cases}\)

Vậy GTNN của B là 2017 khi x = 1; y = -3

Answer 2

\(B=\left(x-1\right)^{2016}+\left|y+3\right|+2017\)

Vì: \(\left(x-1\right)^{2016}\ge0;\left|y+3\right|\ge0\)

=> \(\left(x-1\right)^{2016}+\left|y+3\right|\ge0\)

=> \(\left(x-1\right)^{2016}+\left|y+3\right|+2017\ge2017\)

Vậy GTNN của B là 2017 khi x=1;y=-3