ĐKXĐ : \(x\ge0\)và \(y\ge1\)
\(x+y+12=4\sqrt{x}+6\sqrt{y-1}\)
\(x+y+12-4\sqrt{x}-6\sqrt{y-1}=0\)
\(\left(x-4\sqrt{x}+4\right)+\left(y-1-6\sqrt{y-1}+9\right)=0\)
\(\left(\sqrt{x}-2\right)^2+\left(\sqrt{y-1}-3\right)^2=0\)
\(\Leftrightarrow\hept{\begin{cases}\left(\sqrt{x}-2\right)^2=0\\\left(\sqrt{y-1}-3\right)^2=0\end{cases}}\)( Vì \(\left(\sqrt{x}-2\right)^2\ge0\forall x\) và \(\left(\sqrt{y-1}-3\right)^2\ge0\forall y\))
\(\Leftrightarrow\hept{\begin{cases}\sqrt{x}-2=0\\\sqrt{y-1}-3=0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}\sqrt{x}=2\\\sqrt{y-1}=3\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=4\\y-1=9\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=4\\y=10\end{cases}}\)
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