1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A simple question?

  1. Jun 20, 2006 #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
    (m-n)(1-m-n)=a-b
    But I dunno know what to do next. Plz help.
     

    Attached Files:

    • eq.JPG
      eq.JPG
      File size:
      1.5 KB
      Views:
      48
  2. jcsd
  3. Jun 21, 2006 #2

    HallsofIvy

    User Avatar
    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. Jul 6, 2006 #3
    sqrt(x)+y=a
    Sqrt(y)+x=b

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

    sqrt(x)=a-y
    sqrt(y)=b-x

    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: A simple question?
  1. Simple question (Replies: 5)

  2. Simple Question (Replies: 0)

  3. Simple Question (Replies: 4)

  4. A simple question (Replies: 3)

Loading...