Question

So sánh √27 -√35 và 6-√51

Answer 1

\(\sqrt[]{27}-\sqrt[]{35}\) và \(6-\sqrt[]{51}\)

Giả sử \(\sqrt[]{27}-\sqrt[]{35}< 6-\sqrt[]{51}\)

\(\Leftrightarrow27-2.\sqrt[]{27.35}+35< 36-12\sqrt[]{51}+51\)

\(\Leftrightarrow63-6.\sqrt[]{105}< 87-12\sqrt[]{51}\)

\(\Leftrightarrow12\sqrt[]{51}-6.\sqrt[]{105}< 24\)

\(\Leftrightarrow6\sqrt[]{3}\left(\sqrt[]{17}-\sqrt[]{35}\right)< 24\)

\(\Leftrightarrow\sqrt[]{3}\left(\sqrt[]{17}-\sqrt[]{35}\right)< 4\)

mà \(\sqrt[]{17}-\sqrt[]{35}< 0\)

\(\Leftrightarrow\sqrt[]{3}\left(\sqrt[]{17}-\sqrt[]{35}\right)< 0< 4\left(đúng\right)\)

Vậy \(\sqrt[]{27}-\sqrt[]{35}< 6-\sqrt[]{51}\)