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Simultaneous equations

  1. Sep 8, 2011 #1
    1. The problem statement, all variables and given/known data
    2 positive numbers , x and y, are such that the sum of their squares is 10 times their sum.

    a. write an equation to link x and y
    b. If y is the larger number and the difference is 6 show that x satisfies the equation
    x2-4x-12=0
    c. solve the equation and fin the 2 positive numbers x and y



    2. Relevant equations



    3. The attempt at a solution
    Part a. This is where I think I may be wrong

    10x+10y=x2+y2

    Part b. y= x+6, substitute in above formula, but I can't get the same quadratic equation as the question.

    Part c. I can do this ok.
     
  2. jcsd
  3. Sep 8, 2011 #2

    Borek

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    Staff: Mentor

    Check your math then. Or show it, so that someone can help checking.
     
  4. Sep 8, 2011 #3
    So then after substituting

    10x+10x+60=x^2+(x+6)^2

    work that all out and collect the terms

    20x+60=4x^2+36+24x

    then set the equation equal to zero

    4x^2-4x-24=0

    divide by 4

    x^2-x-6=0

    But thats not what it says to show in the question
     
  5. Sep 8, 2011 #4

    Borek

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    Staff: Mentor

    You right side is off, what is [itex](a+b)^2[/itex] equal to?
     
  6. Sep 8, 2011 #5
    a^2+2ab+b^2
     
  7. Sep 8, 2011 #6
    seen it now, thanks
     
  8. Sep 8, 2011 #7

    Borek

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    Staff: Mentor

    And [itex](x+6)^2[/itex]?

    And [itex]x^2+(x+6)^2[/itex]?

    Edit: OK, I guess you found the problem :smile:
     
  9. Sep 8, 2011 #8
    x^2+12x+36

    2x^2 +12x+36
     
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