Đk: \(x\ge\dfrac{5}{2}\)
\(\sqrt{x-2+\sqrt{2x-5}}+\sqrt{x+2+3\sqrt{2x-5}}=7\sqrt{2}\)
\(\Leftrightarrow\sqrt{2x-4+2\sqrt{2x-5}}+\sqrt{2x+4+6\sqrt{2x-5}}=14\)
\(\Leftrightarrow\left|\sqrt{2x-5}+1\right|+\left|\sqrt{2x-5}+3\right|=14\)
\(\Leftrightarrow\sqrt{2x-5}+1+\sqrt{2x-5}+3=14\)
\(\Leftrightarrow2\sqrt{2x-5}=10\)
\(\Leftrightarrow\sqrt{2x-5}=5\)
\(\Leftrightarrow2x-5=25\)
\(\Leftrightarrow2x=30\)
\(\Leftrightarrow x=15\left(N\right)\)
Kl: x=15
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