Question

\(\sqrt{x^2-6x+9}-\dfrac{\sqrt{6}+\sqrt{3}}{\sqrt{2}+1}=0\)

Answer 1

\(\sqrt{x^2-6x+9}-\dfrac{\sqrt{6}+\sqrt{3}}{\sqrt{2}+1}=0\)

\(\Leftrightarrow\sqrt{\left(x-3\right)^2}-\dfrac{\sqrt{3}\left(\sqrt{2}+1\right)}{\sqrt{2}+1}=0\)

\(\Leftrightarrow\left|x-3\right|-\sqrt{3}=0\Leftrightarrow\left|x-3\right|=\sqrt{3}\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=\sqrt{3}\\x-3=-\sqrt{3}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3+\sqrt{3}\\x=3-\sqrt{3}\end{matrix}\right.\)

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