A simple question?

  1. :smile: Hi Everbody,
    I am a new member to this forum.I am from INDIA and studying in grade 12.
    I was struck in a question and need help.Hope someone could solve it.
    The question is to solve these simultaneous equations:-
    √x + y = a -------- (i)
    x +√y = b ---------- (ii)

    I have a few hints such as making a change in variable by introducing
    x = m^2 and y= n^2 and then doing some algebraic manipulations to get
    But I dunno know what to do next. Plz help.

    Attached Files:

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  2. jcsd
  3. HallsofIvy

    HallsofIvy 41,055
    Staff Emeritus
    Science Advisor

    Those "algebraic manipulations" don't help because you are left with one equation in two variables. After you have m2+ n= b and m+ n2= a, you can solve the first for n: n= b- m2 and then substitute in the second: m+ (b-m2)2= a. That gives a single, fourth degree, equation for m.
    Last edited: Jun 21, 2006
  4. sqrt(x)+y=a

    I'd simply...use a substitution after working around w/ them


    x=a^2 - 2ay + y^2
    y=b^2 -2bx + x^2

    And now...stick the x into the y=

    y=B^2 -2b(a^2 - 2ay + y^2) + (a^2 - 2ay + y^2)^2
    And algebrate. it's ugly but you can't dodge the forth power I don't think. SUbstitute y from both sides and you'll have the =0
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