30.已知a^2/3+b^2/3=4,x=a+3a^1/3b^2/3,y=b+3a^2/3b^1/3,求(x+y)^2/3+(x-y)^2/3

问题描述:

30.已知a^2/3+b^2/3=4,x=a+3a^1/3b^2/3,y=b+3a^2/3b^1/3,求(x+y)^2/3+(x-y)^2/3

8
x+y=(a^1/3+b^1/3)^3
x-y=(a^1/3-b^1/3)^3
(x+y)^2/3+(x-y)^2/3=(a^1/3+b^1/3)^2+(a^1/3-b^1/3)^2=2(a^2/3+b^2/3)=8