\(A=\left|x+5\right|+\left|x-5\right|=\left|x+5\right|+\left|5-x\right|\)
Áp dụng BĐT:
\(\left|A\right|+\left|B\right|\ge\left|A+B\right|\)
\(\Rightarrow A\ge\left|x+5+5-x\right|\)
\(\Rightarrow A\ge10\)
Dấu "=" xảy ra khi:
\(-5\le x\le5\)
\(M=1,5-\left|x+1,1\right|\)
\(\left|x+1,1\right|\ge0\)
\(\Rightarrow A=1,5-\left|x+1,1\right|\le1,5\)
Dấu"=" xảy ra khi:
\(\left|x+1,1\right|=0\Rightarrow x+1,1=0\Rightarrow x=-1,1\)
\(\Rightarrow M_{MAX}=1,5\)
\(N=-3,7-\left|1,7-x\right|\)
\(\left|1,7-x\right|\ge0\)
\(\Rightarrow-3,7-\left|1,7-x\right|\le-3,7\)
Dấu "=" xảy ra khi:
\(\left|1,7-x\right|=0\Rightarrow1,7-x=0\Rightarrow x=1,7\)
\(\Rightarrow N_{MAX}=-3,7\)
1,
\(A=\left|x+5\right|+\left|x-5\right|=\left|x+5\right|+\left|5-x\right|\)
Áp dụng tính chất dãy tỉ số bằng nhau có:
\(A=\left|x+5\right|+\left|5-x\right|\ge\left|x+5+5-x\right|=\left|10\right|=10\)
Dấu " = " khi \(\left\{{}\begin{matrix}x+5\ge0\\5-x\ge0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x\ge-5\\x\le5\end{matrix}\right.\)
Vậy \(MIN_A=10\) khi \(-5\le x\le5\)
2,
a, \(M=1,5-\left|x+1,1\right|\le1,5\)
Dấu " = " khi \(\left|x+1,1\right|=0\Rightarrow x=-1,1\)
Vậy \(MAX_M=1,5\) khi x = -1,1
b, \(N=-3,7-\left|1,7-x\right|\le-3,7\)
Dấu " = " khi \(\left|1,7-x\right|=0\Rightarrow x=1,7\)
Vậy \(MAX_N=-3,7\) khi x = 1,7
