Question

Giải Phương trình:

\(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=1\)

Answer 1

\(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=1\)(ĐK:\(x\ge1\))

\(\Leftrightarrow\sqrt{x-1-4\sqrt{x-1}+4}+\sqrt{x-1-6\sqrt{x+1+9}=1}\)

\(\Leftrightarrow\sqrt{\left(\sqrt{x-1}-2\right)^2}+\sqrt{\left(\sqrt{x-1}-3\right)^2}=1\)

Xét \(0\le\sqrt{x-1}< 2\)

\(\Leftrightarrow2-\sqrt{x-1}+3-\sqrt{x-1}=1\)

\(\Leftrightarrow\sqrt{x-1}=2\)(loại)

Xét \(2\le\sqrt{x-1}< 3\Leftrightarrow5\le x< 10\)

\(\Leftrightarrow\sqrt{x-1}-2+3-\sqrt{x-1}=1\)

\(\Leftrightarrow1=1\)(luôn đúng)

Xét \(\sqrt{x-1}\ge3\)

\(\Leftrightarrow\sqrt{x-1}-2+\sqrt{x-1}-3=1\)

\(\Leftrightarrow\sqrt{x-1}=3\)(tm)

\(\Leftrightarrow x=10\)

Vậy...