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Math Help - Algebra question

  1. #1
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    Algebra question

    Hey, would appreciate any help on this, haven't had any hope with it at all

    we are given the equations
    x^2 = (y^2) +4
    (x+0.95)^2 = ((y+1.05) ^2) +4
    2.1y = 1.9x - 0.2

    The question is to form a quadratic for x and then solve it and then find out terms for y.

    I expanded out the second equation to y^2 - x^2 + 2.1y - 1.9x = -4.2
    h/e everytime i try and replace a y value i end up with -4.2 = -4.2 or something similar.
    It was based on 2 right angle triangles, first with sides 2, x, y
    second with sides 2 , x + 0.95, y + 1.05

    Thanks for any help in advance
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by jono View Post
    Hey, would appreciate any help on this, haven't had any hope with it at all

    we are given the equations
    x^2 = (y^2) +4
    (x+0.95)^2 = ((y+1.05) ^2) +4
    2.1y = 1.9x - 0.2

    The question is to form a quadratic for x and then solve it and then find out terms for y.

    I expanded out the second equation to y^2 - x^2 + 2.1y - 1.9x = -4.2
    h/e everytime i try and replace a y value i end up with -4.2 = -4.2 or something similar.
    It was based on 2 right angle triangles, first with sides 2, x, y
    second with sides 2 , x + 0.95, y + 1.05

    Thanks for any help in advance
    Substitute the third into the first to get:

    <br />
20 x^2 + 19 x - 442=0<br />

    (Note in general three equations in two unknowns has no solution, though that does not
    mean that these equations have no solution)

    RonL
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  3. #3
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    Jun 2007
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    Thanks for the help

    hope im not being too much bother but could anyone explain how to substitute the third into the first? im not entirely sure how
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  4. #4
    Senior Member tukeywilliams's Avatar
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     2.1y = 1.9x-0.2

    So

     y \approx 0.90x - 0.095

    and  x^{2} = y^{2} + 4 = (0.90x - 0.095)^{2} + 4  \approx  19.0000x^{2}+17.10000x -400.902500 (slightly different from CaptainBlack depending on how you round).

    From the following:  (0.90x - 0.095)^{2} + 4 we multiply by 100 to get whole numbers (as CaptainBlack did)
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