Question

已知ab>0,试比较三次根号a-三次根号b与三次根号a-b的大小

Answer 1

[a^(1/3)-b^(1/3)]^3=a-b+3(ab)^(1/3)(a^(1/3-b^(1/3))

[(a-b)^(1/3)]^3=(a-b)

[a^(1/3)-b^(1/3)]^3-[(a-b)^(1/3)]^3

=3(ab)^(1/3)(a^(1/3-b^(1/3)) （1）

因ab>0 所以当a>b>0,或0(a-b)^(1/3)

当b>a>0,或0