Question

So sánh các số: 

          \(\frac{30-2\sqrt{45}}{4}\)với  \(\sqrt{17}\)

Answer 1

Giả sử

\(\frac{30-2\sqrt{45}}{4}>\sqrt{17}\)

\(\Leftrightarrow15>2\sqrt{17}+\sqrt{45}\)

\(\Leftrightarrow225>113+4\sqrt{765}\)

\(\Leftrightarrow28>\sqrt{765}\)

\(\Leftrightarrow784>765\) (đúng)

Vậy \(\frac{30-2\sqrt{45}}{4}>\sqrt{17}\)

Answer 2

Giả sử:

\(\frac{30-2\sqrt{45}}{4}>\sqrt{17}\)

\(\Leftrightarrow15>2\sqrt{17}+\sqrt{45}\)

\(\Leftrightarrow225>113+4\sqrt{765}\)

\(\Leftrightarrow28>\sqrt{765}\)

\(\Leftrightarrow784>765\)(đúng)

Vậy \(\frac{30-2\sqrt{45}}{4}>\sqrt{17}\)