Question

Tìm giá trị nhỏ nhất của biểu thức H = 2019 - |x - y|²⁰¹⁸ - | 2x+1| - | 4x+2|

Answer 1

\(H=2019-\left(\left|x-y\right|^{2018}+\left|2x+1\right|+\left|4x+2\right|\right)\)

+ \(\left\{{}\begin{matrix}\left|x-y\right|^{2018}\ge0\forall x,y\\\left|2x+1\right|\ge0\forall x\\\left|4x+2\right|\ge0\forall x\end{matrix}\right.\)

\(\Rightarrow\left|x-y\right|^{2018}+\left|2x+1\right|+\left|4x+2\right|\ge0\forall x,y\)

\(\Rightarrow H\le2019\forall x,y\)

+ H = 2019 \(\Leftrightarrow\left\{{}\begin{matrix}\left|x-y\right|^{2018}=0\\\left|2x+1\right|=0\\\left|4x+2\right|=0\end{matrix}\right.\Leftrightarrow x=y=-\frac{1}{2}\)

Vậy Min H = 2019 \(\Leftrightarrow x=y=-\frac{1}{2}\)