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Math Help - Clculate a^2+b^2

  1. #1
    Super Member dhiab's Avatar
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    Clculate a^2+b^2

    If : (a^{3}=3ab^{2}+11)and(b^{3}=3a^{2}b+2)
    Calculate : a^{2}+b^{2}
    a, b in R.( no calculate a,b).
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  2. #2
    Senior Member AllanCuz's Avatar
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    Quote Originally Posted by dhiab View Post
    If : (a^{3}=3ab^{2}+11)and(b^{3}=3a^{2}b+2)
    Calculate : a^{2}+b^{2}
    a, b in R.( no calculate a,b).
    hmm..

     a^3 + b^3 = (a+b)(a^2 - ab +b^2)

     a^3 + b^3 = 3ab^2 + 11 + 3a^2 b + 2

     a^2 - ab +b^2 = \frac{ 3(ab^2 + a^2b) +13 }{ a+b }

     a^2 + b^2 = \frac{ 3(ab^2 + a^2b) +13 }{ a+b } + ab

     a^2 + b^2 = \frac{ 3(ab^2 + a^2b) +13 + a^2b + b^2a}{ a+b }

     a^2 + b^2 = \frac{ 4(ab^2 + a^2b) +13 }{ a+b }

    Does the question want the above in terms of a value (i.e. right side cant have a or b in it)?
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  3. #3
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    Quote Originally Posted by dhiab View Post
    If : (a^{3}=3ab^{2}+11)and(b^{3}=3a^{2}b+2)
    Calculate : a^{2}+b^{2}
    a, b in R.( no calculate a,b).
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  4. #4
    Member arpitagarwal82's Avatar
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    Very smart solution essafty.
    Where is the thanks button gone??
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  5. #5
    Super Member Bacterius's Avatar
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    Nicely done, Essafty ! Well presented, too. If there was a thanks button I'd be hitting it
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  6. #6
    Senior Member pacman's Avatar
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    <essafty>

    what a clever solution you have shown . . . . i like it
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