Question

[Linh Nguyễn]

1) Tìm GTNN của các biểu thức:

a) P= (|x-3|+2)² + |y+3|+2007

b) Q= |x-2008| + |x-2009|

3) A= |2x-2|+|2x-2013|

4) B= |2013-x| + |2014-x|

5) C= |x-2014|+|2015-x|+|x-2016|

6) D= |x-2|+|x-9|+|x+1945|

Answer 1

[holicuoi]

x+2/2013+x+1/2014=x/2015+x-1/2016

Answer 2

[Ngu Ngu Ngu]

a) \(\left(\left|x-3\right|+2\right)^2+\left|y+3\right|=2007\)

Ta có: \(\left|x-3\right|\ge0\forall x\)

\(\Rightarrow\left(\left|x-3\right|+2\right)^2\ge\left(0+2\right)^2=2^2=4\)

Lại có: \(\left|y+3\right|\ge0\forall y\)

\(\Rightarrow\left(\left|x-3\right|+2\right)^2+\left|y+3\right|\ge4+0=4\)

\(\Rightarrow\left(\left|x-3\right|+2\right)^2+\left|y+3\right|+2007\ge4+2007=2011\)

 \(\Rightarrow P_{MIN}=2011\)

Dấu "=" xảy ra khi \(\Leftrightarrow\orbr{\begin{cases}\left|x-3\right|=0\\\left|y+3\right|=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=3\\y=-3\end{cases}}}\)

Vậy \(P_{MIN}=2011\) tại \(\orbr{\begin{cases}x=3\\y=-3\end{cases}}\)