Question

\(CMR:\left|x-2015\right|+\left|2016-x\right|\ge1\)

Answer 1

cute thế bn ơi tick nha mk ko bít lm mk hok loqps 5

Answer 2

Ta có: |x-2015|+|2016-x|>=|x-2015+2016-x|=1(theo công thức : |A|+|B|>=|A+B|

=>đpcm

Answer 3

Đặt \(\left|x-2015\right|+\left|2016-x\right|\)

Nếu \(x<2015\) thì:

\(A=2015-x+x-2016=4031-2x\)

Do \(x<2015\Rightarrow-2x>-4032\)

Nếu \(x>2016\) thì 

\(A=x-2015+x-2016=2x-4031\)

Do \(x>2016\Leftrightarrow2x>4032n\text{ê}n\text{A}>1\)

Nếu \(2015\le x\le2016\) thì

\(A=x-2015+2016-x=1\)

Vậy: \(A=\left|x-2015\right|+\left|2016-x\right|\ge1\)

Answer 4

xét x<2015:

=>M=2016-x-(x-2015)

=2016-x-x+2015

=2016+2015-2x>2016+2015-2015.2=1

xét 2015<(=)x<(=)2016:

=>M=x-2015+2016-x=1

xét x>2016:

=>M=x-2015-(2016-x)

=x-2015-2016+x=2x-2015-2016>2016.2-2015.2016=1

=>lx-2015l+l2016-xl>(=)1

=>đpcm