\(a.\sqrt{x^2-2x+5}=x+1\left(x\ge-1\right)\)
\(\Leftrightarrow x^2-2x+5=x^2+2x+1\)
\(\Leftrightarrow4x=4\)
\(\Leftrightarrow x=1\left(TM\right)\)
KL....
\(b.\sqrt{x^2+5x-2}=x-3\left(x\ge3\right)\)
\(\Leftrightarrow x^2+5x-2=x^2-6x+9\)
\(\Leftrightarrow11x=11\)
\(\Leftrightarrow x=1\left(KTM\right)\)
KL.....
\(c.\sqrt{x^2-1}+1=x^2\)
\(\Leftrightarrow\sqrt{x^2-1}=x^2-1\left(ĐKXĐ:\left[{}\begin{matrix}x\ge1\\x\le-1\end{matrix}\right.\right)\)
\(\Leftrightarrow\sqrt{x^2-1}\left(1-\sqrt{x^2-1}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2-1=0\\1-\sqrt{x^2-1}=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\pm1\left(TM\right)\\x=\sqrt{2}\left(TM\right)\end{matrix}\right.\)
KL.....
\(d.x-\sqrt{x^4-2x^2+1}=1\)
\(\Leftrightarrow\sqrt{x^4-2x^2+1}=x-1\left(x\ge1\right)\)
\(\Leftrightarrow\left|x^2-1\right|=x-1\circledast\)
Do : \(x\ge1\Rightarrow x^2-1\ge0\)
\(\circledast\Leftrightarrow x^2-1=x-1\Leftrightarrow x\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\left(KTM\right)\\x=1\left(TM\right)\end{matrix}\right.\)
KL.....
