\(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}\)
\(=\sqrt{x-1+2\sqrt{x-1}+1}+\sqrt{x-1-2\sqrt{x-1}+1}\)
\(=\sqrt{\left(\sqrt{x-1}+1\right)^2}+\sqrt{\left(\sqrt{x-1}-1\right)^2}=\left|\sqrt{x-1}+1\right|+\left|\sqrt{x-1}-1\right|\)
Xét \(x\ge2\Rightarrow\sqrt{x-1}\ge1\Rightarrow\left|\sqrt{x-1}+1\right|+\left|\sqrt{x-1}-1\right|\)
\(=\sqrt{x-1}+1+\sqrt{x-1}-1=2\sqrt{x-1}\)
Xét \(x< 2\Rightarrow\sqrt{x-1}< 1\Rightarrow\left|\sqrt{x-1}+1\right|+\left|\sqrt{x-1}-1\right|\)
\(=\sqrt{x-1}+1+1-\sqrt{x-1}=2\)
Câu mấy á bạn ?
P/s: Chỉ đc hỏi 1 câu thôi nhá!
a) \(\dfrac{a-b}{\sqrt{a}-\sqrt{b}}=\sqrt{a}+\sqrt{b}\)
\(\dfrac{x-2\sqrt{x}+1}{\sqrt{x}-1}=\sqrt{x}-1\)
b) \(\sqrt{4+\sqrt{7+4\sqrt{3}}}=\sqrt{4+2+\sqrt{3}}=\sqrt{6+\sqrt{3}}\)
\(\sqrt{5+\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
\(=\sqrt{5+\sqrt{3}+5\sqrt{48-20-10\sqrt{3}}}\)
\(=\sqrt{5+\sqrt{3}+5\sqrt{28-10\sqrt{3}}}\)
\(=\sqrt{5+\sqrt{3}+5\left(5-\sqrt{3}\right)}\)
\(=\sqrt{5+\sqrt{3}+25-5\sqrt{3}}\)
\(=\sqrt{30-4\sqrt{3}}\)
