Question

So sánh: \(\sqrt{2007}-\sqrt{2006}\) và \(\frac{1}{2\sqrt{2006}}\)

Answer 1

\(\sqrt{2007}-\sqrt{2006}=\frac{\sqrt{2007}-\sqrt{2006}}{2007-2006}=\frac{\sqrt{2007}-\sqrt{2006}}{\left(\sqrt{2007}-\sqrt{2006}\right)\left(\sqrt{2007}+\sqrt{2006}\right)}\)

\(=\frac{1}{\sqrt{2007}+\sqrt{2006}}< \frac{1}{\sqrt{2006}+\sqrt{2006}}=\frac{1}{2\sqrt{2006}}\)

Vậy \(\sqrt{2007}-\sqrt{2006}< \frac{1}{2\sqrt{2006}}\)

Answer 2

Bạn áp dùng biểu thức liên hợp là được

Ta có :

\(\sqrt{2007}-\sqrt{2006}=\frac{1}{\sqrt{2007}+\sqrt{2006}}\)(1)

\(\frac{1}{2\sqrt{2006}}=\frac{1}{\sqrt{2006}+\sqrt{2006}}\)(2)

Từ (1)(2)=>\(\frac{1}{\sqrt{2007}+\sqrt{2006}}< \frac{1}{\sqrt{2006}+\sqrt{2006}}\)

\(\Rightarrow\sqrt{2007}-\sqrt{2006}>\frac{1}{2\sqrt{2006}}\)