若A^2/3+B^2/3=4,X=A+3A^1/3B^2/3,Y=B+A^2/3B^1/3
问题描述：
若A^2/3+B^2/3=4,X=A+3A^1/3B^2/3,Y=B+A^2/3B^1/3
计算（x+y)^2/3+(x-y)^2/3的值!
答
X=A+3A^1/3B^2/3,Y=B+A^2/3B^1/3?
不是Y=B+3A^2/3B^1/3?
如果是Y=B+3A^2/3B^1/3
X+Y=A+B+3A^1/3B^2/3+3A^2/3B^1/3=(A^1/3+B^1/3)(A^2/3-A^1/3B^1/3+B^2/3)+3A^1/3B^1/3(A^1/3+B^1/3)
=(A^1/3+B^1/3)(A^2/3-A^1/3B^1/3+3A^1/3B^1/3+B^2/3)
=(A^1/3+B^1/3)(A^2/3+2A^1/3B^1/3+B^2/3)
=(A^1/3+B^1/3)^3
X-Y=A-B+3A^1/3B^2/3-3A^2/3B^1/3=(A^1/3-B^1/3)(A^2/3+A^1/3B^1/3+B^2/3)-3A^1/3B^1/3(A^1/3-B^1/3)
=(A^1/3-B^1/3)(A^2/3+A^1/3B^1/3-3A^1/3B^1/3+B^2/3)
=(A^1/3-B^1/3)(A^2/3-2A^1/3B^1/3+B^2/3)
=(A^1/3-B^1/3)^3
所以(X+Y))^2/3+(X-Y)^2/3
=[(A^1/3+B^1/3)^3]^2/3+[(A^1/3-B^1/3)^3]^2/3
=(A^1/3+B^1/3)^2+(A^1/3-B^1/3)^2
=A^2/3+2A^1/3B^1/3+B^2/3+A^2/3-2A^1/3B^1/3+B^2/3
=2A^2/3+2B^2/3