\(\sqrt{x+4\sqrt{x}+4}=3\)
Bài làm :
\(\Leftrightarrow\sqrt{\left(\sqrt{x}\right)^2+2.\sqrt{x}.2+2^2}=3\)
\(\Leftrightarrow\sqrt{\left(\sqrt{x}+2\right)^2}=3\)
Vì \(\left(\sqrt{x}+2\right)^2\ge0\) với mọi x
\(\Rightarrow\left|\sqrt{x}+2\right|=\sqrt{x}+2\)
\(\Rightarrow\sqrt{x}+2=3\)
\(\Rightarrow\sqrt{x}=1\)
\(\Rightarrow\left(\sqrt{x}\right)^2=1^2=>x=1\)
\(\sqrt{x\:+4\sqrt{x}+4}\) =3
\(\Leftrightarrow\) \(\sqrt{\left(\sqrt{x}+2\right)^2}\) = 3
\(\Leftrightarrow\) \(\left|\sqrt{x}+2\right|\) =3
\(\Leftrightarrow\) \(\left[{}\begin{matrix}\sqrt{x}+2=3\\\sqrt{x}+2=-3\end{matrix}\right.\) \(\Leftrightarrow\)\(\left[{}\begin{matrix}\sqrt{x}=1\left(TM\right)\\\sqrt{x}=-5\left(KTM\right)\end{matrix}\right.\) \(\Leftrightarrow\) x=1
\(=>\sqrt{\left(\sqrt{x}-2\right)^2}=3\\ ->\\ \sqrt{x}-2=3->x=25\)
