Bài 1 Từ \(\left|x-1\right|=2\) \(\Rightarrow\left\{{}\begin{matrix}x-1=2\\x-1=-2\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}x=2+1\\x=-2+1\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)
Với x = 3 \(\Rightarrow A=3\cdot3^2-4\cdot3+1\)
\(A=3\cdot9-12+1\)
\(A=27-12+1=16\)
Với x = -1 \(\Rightarrow A=3\cdot\left(-1\right)^2-4\cdot\left(-1\right)+1\)
\(A=3\cdot1-\left(-4\right)+1\)
\(A=3+4+1=8\)
Bài 2
a) \(\left|x-10\right|=-x+10=10-x\)
\(\left|x-10\right|=10-x\) \(\Leftrightarrow x-10\le0\) \(\Leftrightarrow x\le10\)
b)\(\left|\dfrac{x-1}{1-x}\right|=1\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x-1}{1-x}=1\\\dfrac{x-1}{1-x}=-1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x-1=1-x\\x-1=-1+x\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}x+x=1+1\\x-x=-1+1\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}2x=2\\0=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=2:2=1\\x\in Z\end{matrix}\right.\)
d)\(\left|x-4\right|+\left(3+3\right)=7\)
\(\left|x-4\right|+6=7\)
\(\left|x-4\right|=7-6\)
\(\left|x-4\right|=1\)
\(\Rightarrow\left\{{}\begin{matrix}x-4=1\\x-4=-1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=1+4\\x=-1+4\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}x=5\\x=3\end{matrix}\right.\)
