Question

Tìm Min P = /x+4/ +/x+7/

 

Answer 1

\(P=\left|x+4\right|+\left|x+7\right|=\left|x+4\right|+\left|-\left(x+7\right)\right|\)

Áp dụng bđt \(\left|a\right|+\left| b\right|\ge\left|a+b\right|\)ta có:

\(P\ge\left|x+4-\left(x+7\right)\right|=3\)

Dấu = khi \(\left(x+4\right)\left(x+7\right)\ge0\)\(\Rightarrow-4\le x\le-7\)

\(\Rightarrow\hept{\begin{cases}\left(x+4\right)\left(x+7\right)=0\\-4\le x\le-7\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x=-4\\x=-7\end{cases}}\)

Vậy MinP=3 khi \(\hept{\begin{cases}x=-4\\x=-7\end{cases}}\)