a/ \(\sqrt{x^2-2x+1}=5\)
\(\Leftrightarrow\sqrt{\left(x-1\right)^2}=5\)
\(\Leftrightarrow\left(x-1\right)^2=25\)
\(\Leftrightarrow\left(x-1\right)^2-25=0\)
\(\Leftrightarrow\left(x-1-5\right)\left(x-1+5\right)=0\)
\(\Leftrightarrow\left(x-6\right)\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-6=0\\x+4=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-4\end{matrix}\right.\)
Vậy...
b/ \(\sqrt{x^2+x+1}=1\)
\(\Leftrightarrow x^2+x+1=1\)
\(\Leftrightarrow x^2+x+1-1=0\)
\(\Leftrightarrow x\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)
Vậy....
c/ ĐKXĐ : \(x\ge-2\)
Ta có :
\(\sqrt{x+2}=5\)
\(\Leftrightarrow x+2=25\)
\(\Leftrightarrow x=23\)
Vậy...
d/ \(\sqrt{x^2+1}=3\)
\(\Leftrightarrow x^2+1=9\)
\(\Leftrightarrow x^2+1-9=0\)
\(\Leftrightarrow x^2-8=0\)
\(\Leftrightarrow\left(x-2\sqrt{2}\right)\left(x+2\sqrt{2}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\sqrt{2}\\x=-2\sqrt{2}\end{matrix}\right.\)
Vậy....
e/ ĐKXĐ : \(x\ge1\)
\(3-\sqrt{x-1}=9\)
\(\sqrt{x-1}=-6\) (vô lí)
Vậy...
f/ ĐKXĐ : \(x\ge-5\)
Ta có :
\(\sqrt{x+5}=-2\) (vô lí)
Vậy....
g/ ĐKXĐ : \(x\ge1\)
Ta có :
\(3\sqrt{x-1}=9\)
\(\Leftrightarrow\sqrt{x-1}=3\)
\(\Leftrightarrow x-1=9\)
\(\Leftrightarrow x=10\)
Vậy..
