Question

giải phương trình : \(\sqrt{x+5}+2019\sqrt{x+4}=2019+\sqrt{\left(x+5\right)\left(x+4\right)}\)

Answer 1

ĐKXĐ: \(x\ge-4\)

\(\Leftrightarrow\sqrt{x+5}-\sqrt{\left(x+5\right)\left(x+4\right)}+2019\sqrt{x+4}-2019=0\)

\(\Leftrightarrow\sqrt{x+5}\left(1-\sqrt{x+4}\right)-2019\left(1-\sqrt{x+4}\right)=0\)

\(\Leftrightarrow\left(\sqrt{x+5}-2019\right)\left(1-\sqrt{x+4}\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}\sqrt{x+4}=1\\\sqrt{x+5}=2019\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=-3\\x=2019^2-5\end{matrix}\right.\)