Question

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.

Answer 1

[(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2a