Bài1:
\(\left|x\right|=5\)
\(\Rightarrow x\in\left\{-5;5\right\}\)
Vậy...
\(\left|x\right|+x=4\)
\(\Rightarrow\left|x\right|=4-x\)
+)Xét \(x\ge0\Rightarrow\left|x\right|=x\)
Do đó:
\(x=4-x\)
\(2x=4\Rightarrow x=2\left(chọn\right)\)
+) Xét \(x< 0\Rightarrow\left|x\right|=-x\)
Do đó:
\(-x=4-x\)
\(0x=4\)
\(x\in\varnothing\)
Vậy...
Bài2:
\(\left|x+1\right|+5\)
Với mọi x thì \(\left|x+1\right|\ge0\Rightarrow\left|x+1\right|+5\ge5\)
Để \(\left|x+1\right|+5=5\) thì
\(\left|x+1\right|=0\)
\(x+1=0\)
\(x=-1\)
Vậy...
Bài 1:
a) \(\left|x\right|=5\Rightarrow x=\pm5\)
b) \(\left|x\right|+x=4\Rightarrow\left|x\right|=4-x\)
\(\Rightarrow\left\{{}\begin{matrix}x=4-x\Rightarrow x+x=4\Rightarrow2x=4\Rightarrow x=2\\x=x-4\Rightarrow x-x=-4\Rightarrow0=-4\left(loại\right)\end{matrix}\right.\)
c) \(\left|x+2\right|=5\)
\(\Rightarrow\left\{{}\begin{matrix}x+2=5\Rightarrow x=3\\x+2=-5\Rightarrow x=-7\end{matrix}\right.\)
Bài 2:
Ta có: \(\left|x+1\right|\ge0\forall x\)
\(\Rightarrow\left|x+1\right|+5\ge5\forall x\)
Dấu "=" xảy ra \(\Leftrightarrow x+1=0\Rightarrow x=-1\)
Vậy MIN \(A=5\Leftrightarrow x=-1\)
Bài 2)
\(A=\left|x+1\right|+5\)
\(\forall x\) ta có \(\left|x+1\right|\ge0\Rightarrow\left|x+1\right|+5\ge5\)
\(\)Dấu ''='' xảy ra\(\Leftrightarrow\left|x+1\right|=0\)
\(x=-1\)
Vậy \(Amin=5\Leftrightarrow x=1\)
Chúc Bạn Học Tốt !!!
\(\left|x\right|=5\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-5\end{matrix}\right.\)
\(2\left|x\right|+x=4\)
Với \(x\ge0\) ta có:
\(2x+x=4\)
\(\Rightarrow3x=4\Rightarrow x=\dfrac{4}{3}\)
Với \(x< 0\) ta có:
\(-2x+x=4\)
\(\Rightarrow-x=4\)
\(\Rightarrow x=-4\)
Vậy \(\left[{}\begin{matrix}x=\dfrac{4}{3}\\x=-4\end{matrix}\right.\)
2) \(A=\left|x+1\right|+5\)
\(\left|x+1\right|\ge0\forall x\in R\)
\(A=\left|x+1\right|+5\ge5\)
Dấu "=" xảy ra khi:
\(\left|x+1\right|=0\Rightarrow x=-1\)