a/ ĐKXĐ: \(x\ge-\frac{1}{3}\)
\(\Leftrightarrow\left(x^2-10x+25\right)+\left(3x+1-8\sqrt{3x+1}+16\right)=0\)
\(\Leftrightarrow\left(x-5\right)^2+\left(\sqrt{3x+1}-4\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-5=0\\\sqrt{3x+1}-4=0\end{matrix}\right.\) \(\Rightarrow x=5\)
b/ ĐKXĐ: \(\left\{{}\begin{matrix}x\ge3\\y\ge5\end{matrix}\right.\)
\(\Leftrightarrow x+y=2\sqrt{x-3}+6\sqrt{y-5}-2\)
\(\Leftrightarrow\left(x-3-2\sqrt{x-3}+1\right)+\left(y-5-6\sqrt{y-5}+9\right)=0\)
\(\Leftrightarrow\left(\sqrt{x-3}-1\right)^2+\left(\sqrt{y-5}-3\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x-3}-1=0\\\sqrt{y-5}-3=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=4\\y=14\end{matrix}\right.\)
