若A^2/3+B^2/3=4,X=A+3A^1/3B^2/3,Y=B+A^2/3B^1/3

3个回答

  • 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