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Math Help - equality

  1. #1
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    equality

    1.Transform the expression disappearing the root from the consequent.
    1/(5)1/3-(2)1/3 (1/3 is the exponent)

    2.Prove that for evry real x, y and z it's true:
    (x-y)3+(y-z)3+(z-x)3=3*(x-y)*(y-z)*(z-x)
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  2. #2
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    Quote Originally Posted by blertta View Post
    1.Transform the expression disappearing the root from the consequent.
    1/(5)1/3-(2)1/3 (1/3 is the exponent)

    2.Prove that for evry real x, y and z it's true:
    (x-y)3+(y-z)3+(z-x)3=3*(x-y)*(y-z)*(z-x)
    2. Put x - y = m, y - z = n then z - x = -(m+n)
    LHS = m^3 + n^3 - (m+n)^3 = -3 (mn^2 + nm^2) = -3mn(m+n)
    RHS = 3mn * -(m+n) = LHS.

    I don't understand Q 1.
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  3. #3
    MHF Contributor
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    For the first problem, multiply top and bottom by 5^{2/3} + 5^{1/3}2^{1/3} + 2^{2/3}.

    For the second problem, it's just a matter of multiplying out both sides of the expression. Use binomial expansion on the left side.
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