Question

[Shiro Suu]

So sánh:

\(2^{30}+3^{30}+4^{30}với3\times24^{10}\) 

Answer 1

[Nguyễn Thủy Tiên]

đặt A= 3.24¹⁰=3.(8.3)¹⁰=\(\frac{3}{2}\).2.2³⁰.(\(\frac{3}{2}\))¹⁰ . 2¹⁰ = \(\left(\frac{3}{2}\right)^{11}.2^{41}\)

đặt B=2³⁰+3³⁰ + 4³⁰ =2³⁰ +\(\left(\frac{3}{2}\right)^{30}.2^{30}+2^{60}\)

A-B= \(\frac{3}{2}^{11}.2^{41}-2^{30}-2^{30}.\left(\frac{3}{2}\right)^{30}-2^{60}\)

     =\(2^{30}\left(2^{11}.\left(\frac{3}{2}\right)^{11}-1-\left(\frac{3}{2}\right)^{30}-2^{30}\right)\)

     =\(2^{30}\left(3^{11}-1-\left(\frac{3}{2}\right)^{30}-2^{30}\right)<0\)

\(\Rightarrow B>A\)

nhớ ****