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Math Help - Similarity between equations

  1. #1
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    Similarity between equations

    So I have these two equations:

    x^3 + by + c = 0

    y^3 + bx + d = 0

    where x and y are functions of b, and c and d are constants. The task is to show that y = -x when d = -c. Which should be simple enough,

    y^3 + bx + d = 0
    y^3 + bx - c = 0
    y^3 + bx - c = x^3 + by + c
    -y^3 - bx = x^3 + by

    but to me it looks like there's no way to go further than this, or am I missing something? Thanks! =))
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    Quote Originally Posted by gralla55 View Post
    So I have these two equations:

    x^3 + by + c = 0

    y^3 + bx + d = 0

    where x and y are functions of b, and c and d are constants. The task is to show that y = -x when d = -c. Which should be simple enough,

    y^3 + bx + d = 0
    y^3 + bx - c = 0
    y^3 + bx - c = x^3 + by + c
    -y^3 - bx = x^3 + by

    but to me it looks like there's no way to go further than this, or am I missing something? Thanks! =))
    x^3 + by + c = 0
    y^3 + bx - c = 0
    -----------------
    (x^3+y^3) + b(x+y) = 0


    (x+y)(x^2 -xy+y^2) + b(x+y) = 0

    (x+y)[(x^2 -xy+y^2) + b] = 0

    x+y = 0

    y = -x
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