ĐKXĐ: ...
\(y+2\sqrt{x^2+y}=4x+3\)
\(\Leftrightarrow x^2+y+2\sqrt{x^2+y}+1=x^2+4x+4\)
\(\Leftrightarrow\left(\sqrt{x^2+y}+1\right)^2=\left(x+2\right)^2\)
\(\Leftrightarrow\sqrt{x^2+y}+1=x+2\)
\(\Leftrightarrow\sqrt{x^2+y}=x+1\Leftrightarrow x^2+y=x^2+2x+1\)
\(\Rightarrow y=2x+1\)
Thay vào dưới:
\(\left(x-3\right)\sqrt{2x+5}+\left(2x-3\right)\sqrt{x-1}+2=0\)
\(\Leftrightarrow\left(x-2\right)\sqrt{2x+5}+2\left(x-2\right)\sqrt{x-1}+3-\sqrt{2x+5}+\sqrt{x-1}-1=0\)
\(\Leftrightarrow\left(x-2\right)\left(2x+5\right)+2\left(x-2\right)\sqrt{x-1}-\frac{2\left(x-2\right)}{3+\sqrt{2x+5}}+\frac{x-2}{\sqrt{x-1}+1}=0\)
\(\Rightarrow x=2\Rightarrow y=5\)
