Question

Tìm GTNN của biểu thức: A= (|x-2016| + 2017)/(|x - 2016| + 2018)

Answer 1

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Answer 2

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Answer 3

Ta có:

\(A=\frac{\left|x-2016\right|+2017}{\left|x-2016\right|+2018}=\frac{\left|x-2016\right|+2018-1}{\left|x-2016\right|+2018}=1-\frac{1}{\left|x-2016\right|+2018}\)

Vì \(\left|x-2016\right|\ge0\Rightarrow\left|x-2016\right|+2018\ge2018\Rightarrow\frac{1}{\left|x-2016\right|+2018}\le\frac{1}{2018}\)

=>\(A=1-\frac{1}{\left|x-2016\right|+2018}\ge\frac{2017}{2018}\)

=>\(A_{min}=\frac{2017}{2018}\)<=>|x-2016|=0<=>x-2016=0<=>x=2016