đk: \(x\ge0\)
Ta có: \(\sqrt{x}+2\sqrt{x+3}=x+4\)
\(\Leftrightarrow\left(x+3\right)-2\sqrt{x+3}+1=\sqrt{x}-1\)
\(\Leftrightarrow\sqrt{\left(\sqrt{x-3}-1\right)^2}=\sqrt{x}-1\)
\(\Leftrightarrow\left|\sqrt{x-3}-1\right|=\sqrt{x}-1\)
\(\Leftrightarrow\orbr{\begin{cases}\sqrt{x-3}-1=\sqrt{x}-1\\\sqrt{x-3}-1=1-\sqrt{x}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}\sqrt{x-3}=\sqrt{x}\left(ktm\right)\\\sqrt{x-3}+\sqrt{x}=2\end{cases}}\)
\(\Leftrightarrow x-3+x+2\sqrt{x\left(x-3\right)}=4\)
\(\Leftrightarrow2\sqrt{x^2-3x}=7-2x\)
\(\Leftrightarrow4\left(x^2-3x\right)=\left(7-2x\right)^2\)
\(\Leftrightarrow4x^2-12x=49-28x+4x^2\)
\(\Leftrightarrow16x=49\)
\(\Rightarrow x=\frac{49}{16}\)
\(( \sqrt{x+3}-1)^2\) chứ bạn.
với cả là \(\sqrt{x+3}\) mà có phải \(\sqrt{x-3} \) đâu
