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Math Help - Problem solving with Quadratics

  1. #1
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    Exclamation Problem solving with Quadratics

    Two integers differ by 12 and the sum of their squares is 74. Find the integers.
    The answers are : -7 and 5 or 7 and -5.

    Could you please show me how to work this problem out?
    Last edited by Tessarina; February 12th 2010 at 03:27 PM.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Let the integers be x and y
    Quote Originally Posted by Tessarina View Post
    Two integers differ by 12
    this means x - y = 12

    and the sum of their squares is 74.
    this means x^2 + y^2 = 74

    Find the integers.
    What can you do with the above equations?
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    Let the integers be x and ythis means x - y = 12

    this means x^2 + y^2 = 74

    What can you do with the above equations?
    That is where i got up to, but i dont know how to get to the final answer.
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  4. #4
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    Substitute

    x = y + 12

    into the equation x^2 + y^2 = 74

    yielding (y + 12)^2 + y^2 = 74,

    which can be solved using the quadratic formula.
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  5. #5
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    Quote Originally Posted by icemanfan View Post
    Substitute

    x = y + 12

    into the equation x^2 + y^2 = 74

    yielding (y + 12)^2 + y^2 = 74,

    which can be solved using the quadratic formula.

    Could you please show me the working out to get to the answer?
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  6. #6
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    Hello Tessarina
    Quote Originally Posted by Tessarina View Post
    Could you please show me the working out to get to the answer?
    (y+12)^2+y^2=74

    \Rightarrow y^2+24y+144+y^2=74

    \Rightarrow 2y^2+24y +70=0

    \Rightarrow y^2+12y+35=0

    \Rightarrow (y+5)(y+7)=0

    \Rightarrow y = -5, -7

    \Rightarrow x = y+12 = 7, 5

    So the solutions are (7, -5) and (5, -7).

    Grandad
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