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Intersection of two functions

  1. Apr 29, 2015 #1
    1. The problem statement, all variables and given/known data
    The problem ask for points of intersection of two functions
    2. Relevant equations
    1: 2x+y-4=0
    2: (y^2)-4x=0

    3. The attempt at a solution
    My attempt of solution its in a picture attached below...
    I get stuck in this two equations
    1: ((y^2)/4)+(y/2)-2=0
    2: square root(-4x)-2x+4=0
    What. Can i do whit that two equations
    I ve tried the square formula and given a weir and nonsense result
     
  2. jcsd
  3. Apr 29, 2015 #2

    SammyS

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    No picture included.

    Multiply first equation by 2 then add equations to eliminate x.
     
  4. Apr 29, 2015 #3
    This is the picture of my work IMG_20150429_205217774.jpg
     
  5. Apr 29, 2015 #4
  6. Apr 29, 2015 #5

    SammyS

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    How do you get ##\ y=\sqrt{-4x}\ ## ? Specifically, where does that negative sign come from in under the radical ?
     
  7. Apr 30, 2015 #6

    HallsofIvy

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    That was incorrect. Anyway, much simpler is your first suggestion: Multiply first equation by 2 then add equations to eliminate x.

    Equivalently, multiply the first equation by 2, then write it as 4x= 8- 2y so that the second equation can be written [itex]y^2- 8+ 2y= 0[/itex] or [itex]y^2+ 2y- 8= 0[/itex].
     
  8. Apr 30, 2015 #7
    Thanks i will do that, but what is the point of multiply by 2? Dont change the integrity of the next equation?
     
  9. Apr 30, 2015 #8

    SammyS

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    Multiplying an equation by 2 gives an equivalent equation. Right ?


    If you want to use the method of substitution, it's better to solve one of the equations for x rather than for y. Then substitute that into the other equation. That way you don't take a square root.
     
    Last edited: Apr 30, 2015
  10. Apr 30, 2015 #9
  11. Apr 30, 2015 #10

    SammyS

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  12. Apr 30, 2015 #11
    What is thw diference between this and the above equation? Pictures i mean 1430413143609922626788.jpg
     
  13. Apr 30, 2015 #12

    SammyS

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    Maybe not much? I didn't like the ##\ \sqrt{-4x\ }\ ##. Especially since x had to be positive.


    What is your ultimate goal here?
     
  14. Apr 30, 2015 #13
    Find the x and y intersections, i think this is finally solved, but my only doubt, if is this is posible to solve trought this equation:((y^2)/4)=(4-y)/2
     

    Attached Files:

  15. Apr 30, 2015 #14

    SammyS

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    Why not ?
     
  16. Apr 30, 2015 #15
    If i use the quadratic form whit that equation i get, irrational numbers
     
  17. Apr 30, 2015 #16

    SteamKing

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    You shouldn't.

    Please show your calculations.
     
  18. May 6, 2015 #17
    i went out for vacations, and somehow now its clear for my using the two metods and two equations, i am very grateful for the help, cheers guys :)
     
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