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Math Help - find integers

  1. #1
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    find integers

    Currently I'm learning polynomials, trinomials, and basic factoring. I don't understand this question at all.

    'a' and 'b' are integers. Find the value of a and b, if a^2 - b^2 = 2 1.
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    Quote Originally Posted by DFKnight View Post
    Currently I'm learning polynomials, trinomials, and basic factoring. I don't understand this question at all.

    'a' and 'b' are integers. Find the value of a and b, if a^2 - b^2 = 2 1.
    first we think of the factors of 21 that are integers. ok, we can have 21 = 1*21 or 21 = 7*3. now, file that away, we'll come back to it.

    Now a^2 - b^2 = (a + b)(a - b) ........the difference of two squares

    \Rightarrow (a + b)(a - b) = 21

    now we want (a + b) and (a - b) to be integer factors of 21.

    Let's say they are 7 and 3.

    set a + b = 7
    and a - b = 3

    \Rightarrow \boxed{a = 5} \mbox { and } \boxed{ b = 2}

    this is one solution, there are others.

    we get a new solution set if a + b = 3 and a - b = 7

    and also, if we take the factors to be 1 and 21

    we need more conditions if we want a unique solution
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