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Math Help - Hoping someone can help for once! a^3 = b^3

  1. #1
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    Hoping someone can help for once! a^3 = b^3

    Show that if a^3 = b^3 if and only if a=b

    Suppose a = b

    a^3 = (a)(a)(a)
    =(b)(b)(b)
    =b^3

    Prove other direction using contrapositive:

    Suppose a != b, then a^3 != b^3

    Case 1:
    a>b

    ****I'm a little stuck here, I'm not sure if I'm allowed to say aaa>bbb by assuming a>b

    a^3 = (a)(a)(a)
    >(b)(b)(b)
    =b^3

    a^3 != b^3
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  2. #2
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    Quote Originally Posted by glover_m View Post
    Show that if a^3 = b^3 if and only if a=b
    Suppose that p \ne q\;\& \,p^3  = q^3 , that means 0 = p^3  - q^3  = \left( {p - q} \right)\left( {p^2  + qp + q^2 } \right).
    But because p \ne q this means that it must be \left( {p^2  + qp + q^2 } \right)=0.
    Use the classic quadratic formula to prove p has no real roots.
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  3. #3
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    clutch thnx brah
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  4. #4
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    Quote Originally Posted by glover_m View Post
    clutch thnx brah
    What in the world do those nonsense symbol-strings mean?
    Please use standard English on this forum.
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