Đáp án:
\(12 > \dfrac{{30 + 2\sqrt {45} }}{4}\)
Giải thích các bước giải:
\(\begin{array}{l}
\dfrac{{30 + 2\sqrt {45} }}{4} = \dfrac{{30 + 2.\sqrt {9.5} }}{4} = \dfrac{{30 + 2.3\sqrt 5 }}{4}\\
= \dfrac{{30 + 6\sqrt 5 }}{4} = \dfrac{{15}}{2} + \dfrac{{3\sqrt 5 }}{2}\\
12 = \dfrac{{15}}{2} + \dfrac{9}{2} = \dfrac{{15}}{2} + \dfrac{{3.3}}{2}\\
Do:3 > \sqrt 5 \\
\to \dfrac{9}{2} > \dfrac{{3\sqrt 5 }}{2}\\
\to \dfrac{{15}}{2} + \dfrac{9}{2} > \dfrac{{15}}{2} + \dfrac{{3\sqrt 5 }}{2}\\
\to 12 > \dfrac{{30 + 2\sqrt {45} }}{4}
\end{array}\)
