[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00 即a^(1/3)-b^(1/3)>(a-b)^(1/3) 当b>a>0,或0
a,b都为正时 a a>b 那么三次根号a大于三次根号大于三次根号a-b a,b都为负时 a a>b 那么三次根号a-b大于三次根号a大于三次根号b