a)\(\sqrt{x^2-10x+25}=x+2\)
\(\Leftrightarrow\sqrt{\left(x-5\right)^2}=x+2\)
\(\Leftrightarrow\left|x-5\right|=x+2\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=x+2\\x-5=-x-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-x=5+2\\x+x=5-2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}0x=7\\2x=3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}0x=7\left(lo\text{ạ}i\right)\\x=\dfrac{3}{2}\left(nh\text{ậ}n\right)\end{matrix}\right.\)
vậy
\(b.\sqrt{43-x}=x-1\left(ĐK:43\ge x\ge1\right)\)
\(\Leftrightarrow43-x=x^2-2x+1\)
\(\Leftrightarrow43-x^2+x-1=0\)
\(\Leftrightarrow x^2-x-42=0\)
\(\Leftrightarrow x^2-7x+6x-42=0\)
\(\Leftrightarrow x\left(x-7\right)+6\left(x-7\right)=0\)
\(\Leftrightarrow\left(x-7\right)\left(x+6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=7\left(n\right)\\x=-6\left(l\right)\end{matrix}\right.\)
\(c.\sqrt{x-5}=4\left(ĐK:x\ge5\right)\)
\(\Leftrightarrow x-5=16\)
\(\Leftrightarrow x=21\left(n\right)\)
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