p=1/2又1/2次方 Q=11/3又1/3次方 R=1/4又1/4次方哪一個最大?

P = (1/2)^(1/2)
Q = (1/3)^(1/3)
R = (1/4)^(1/4)

考慮比較 P¹², Q¹² 和 R¹²。

P¹² = (1/2)^(6) = 1/64
Q¹² = (1/3)^(4) = 1/81
R¹² = (1/4)^(3) = 1/64

由於 P¹² = R¹² > Q¹²，
可知 P = R > Q。

P 和 R 皆為最大。

P=1/2又1/2次方=0.70710678118654752440084436210485
Q=11/3又1/3次方=1.542021669727580597697454123262638
R=1/4又1/4次方=0.70710678118654752440084436210485
Q>(P=R)