设a,b是正数,比较(a3次方+b3次方)的1/3的次方与(a2次方+b2次方)的1/2的次方.

[(a3次方+b3次方)的1/3的次方]^6
=(a^3+b^3)^2
=a^6+2a^3b^3+b^6

[(a2次方+b2次方)的1/2的次方]^6
=(a^2+b^2)^3
=a^6+3a^4b^2+3a^2b^4+b^6

因为:
(a^6+2a^3b^3+b^6)-(a^6+3a^4b^2+3a^2b^4+b^6)
=2a^3b^3-3a^4b^2-3a^2b^4
=a^2b^2(2ab-3a^2-3b^2)
因为2ab<=a^2+b^2<3(a^2+b^2)
所以:
(a^6+2a^3b^3+b^6)<(a^6+3a^4b^2+3a^2b^4+b^6)
(a3次方+b3次方)的1/3的次方<(a2次方+b2次方)的1/2的次方

(a3次方+b3次方)的1/3次方 < (a2次方+b2次方)的1/2次方