Question

Giải PT:

Answer 1

ĐKXĐ : \(\left\{{}\begin{matrix}x\ge-11\\x\ge\sqrt{x+11}\\x\ge-\sqrt{x+11}\end{matrix}\right.\)

Phương trình đã cho tương đương : 

\(x+\sqrt{x+11}+x-\sqrt{x+11}+2\sqrt{\left(x-\sqrt{x+11}\right).\left(x+\sqrt{x+11}\right)=16}\)

\(\Leftrightarrow x+\sqrt{x^2-x-11}=8\)

\(\Leftrightarrow\left\{{}\begin{matrix}x^2-x-11=\left(8-x\right)^2\\x\le8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}15x=75\\x\le8\end{matrix}\right.\Leftrightarrow x=5\) (tm)