a) ĐK: \(x\ge0\)
\(x-12\sqrt{x}+32=0\)
\(\Leftrightarrow\)\(x-4\sqrt{x}-8\sqrt{x}+32=0\)
\(\Leftrightarrow\)\(\left(\sqrt{x}-4\right)\left(\sqrt{x}-8\right)=0\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}\sqrt{x}-4=0\\\sqrt{x}-8=0\end{cases}}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x=16\\x=64\end{cases}}\) (t.m)
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b) ĐK: \(x\ge-\frac{1}{2}\)
\(\sqrt{x^2-x+9}=2x+1\)
\(\Leftrightarrow\)\(x^2-x+9=4x^2+4x+1\)
\(\Leftrightarrow\)\(3x^2+5x-8=0\)
\(\Leftrightarrow\)\(3x^2-3x+8x-8\)
\(\Leftrightarrow\)\(\left(x-1\right)\left(3x+8\right)\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x=1\\x=-\frac{8}{3}\left(L\right)\end{cases}}\)
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