如何证明这三个数是无理数?5^(1/3)-3^(1/3) ln2 2^(2^(1/2))
问题描述：
如何证明这三个数是无理数?
5^(1/3)-3^(1/3)
ln2
2^(2^(1/2))
答
1.假设5^(1/3)-3^(1/3)是有理数,则存在整数m,n使得5^(1/3)-3^(1/3) = m/n 5^(1/3) = m/n + 3^(1/3) 等式两边立方5 = m^3/n^3 + 3 + 3*m^2/n^2* 3^(1/3) + 3*m/n*3^(2/3)整理2-m^3/n^3 = 3*m^2/n^2* 3^(1/3) + 3*m/n*...