Question

Cho M= \(x-2\sqrt{x-1}\) .Tìm GTNN

Answer 1

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

\(\Rightarrow M=\left(\sqrt{x-1}-1\right)^2\ge0\)

Vậy Min M = 0 khi \(\sqrt{x-1}-1=0\Rightarrow\sqrt{x-1}=1\Rightarrow x=2\)

Answer 2

M = \(x-1-2\sqrt{x-1}+1=\left(\sqrt{x-1}-1\right)^2\ge0\)

Vậy GTNN là 0 tại \(\sqrt{x-1}=1\Leftrightarrow x=2\)