`\sqrt{x+2\sqrt{2x-4}}=5` `ĐK: x >= 2`
`<=>x+2\sqrt{2x-4}=25`
`<=>2\sqrt{2x-4}=25-x` `(2 <= x <= 25)`
`<=>8x-16=625-50x+x^2`
`<=>x^2-58x+641=0`
`<=>x^2-2x.29+841-200=0`
`<=>(x-29)^2=200`
`<=>|x-29|=10\sqrt{2}`
`<=>x=29+-10\sqrt{2}`
Mà `2 <= x <= 25`
`=>x=29-10\sqrt{2}`
ĐKXĐ \(x\ge2\)
\(\sqrt{x+2\sqrt{2x-4}}=5\)
\(\Leftrightarrow\sqrt{x-2+2\sqrt{2}.\sqrt{x-2}+2}=5\)
\(\Leftrightarrow\sqrt{\left(\sqrt{x-2}+\sqrt{2}\right)^2}=5\)
\(\Leftrightarrow\left|\sqrt{x-2}+\sqrt{2}\right|=5\)
\(\Leftrightarrow\sqrt{x-2}+\sqrt{2}=5\)
\(\Leftrightarrow\sqrt{x-2}=5-\sqrt{2}\)
\(\Rightarrow x=29-10\sqrt{2}\)
