Question

[Akira Kinomoto]

tim gia tri nho nhat cua bieu thuc \(A=|x-2016|+x-1\)

Answer 1

[Nguyệt]

ghi thiếu cmnr đề r :>

\(A=\left|x-2016\right|+\left|x-1\right|=\left|x-2016\right|+\left|-x+1\right|\ge\left|x-2016-x+1\right|\)

\(\Leftrightarrow A\ge\left|2015\right|=2015\)

dấu "=" xảy ra khi \(\left(x-2016\right).\left(-x+1\right)\ge0\)

=> \(1\le x\le2016\)

Vậy Min A =2015 khi và chỉ khi \(1\le x\le2016\)

Answer 2

[đăng việt cường]

Nếu  x < 2016 =>\(|x-2016|=2016-x\) .

Khi đó: A=2016-x+x-1=2015

Nếu  \(x\ge2016\) =>\(|x-2016|=x-2016\) .

Khi đó: A=x-2016+x-1=2.x-2017 \(\ge2.2016-2017=2015\)

Vậy Amin=2015 \(\Leftrightarrow\)x=2016.