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Pre-Calculus

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If the sum of two numbers is 1 and the sum of the cubes of the numbers is 3, what is the sum of the squares of the numbers?

  • Pre-Calculus -

    m+n=1
    m^3+n^3=1

    What if one number is zero, so the other number is ....

  • Pre-Calculus -

    No, the sum of the cubes is 3 so its m+n=1 m^3+n^3=3

  • Pre-Calculus -

    oooppppssss
    m+n=1
    m^3+n^3=3
    If you factor the second equation..
    (M+n)(M^2-mn+n^2) the first term is 1, so
    (m^2+n^2 -mn)=3 equation1
    but if we square the first equation given
    m^2+2mn+n^2 = 1
    m^2+n^2+2mn=1 equation2
    subtracting equation2 from equation1
    -mn-2mn=2
    or -3mn=2


    OK, this is not making sense. Check my work, I will try again later.

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