Please turn on javascript in your browser to play chess.
Posers and Puzzles

Posers and Puzzles

  1. Subscriber joe shmo On Vacation
    Strange Egg
    17 Jan '08 04:47 / 1 edit
    how is

    y = sqrt(2x-x^2) solved for x in terms of y?

    I'm getting lost on this one

    here is what i come up with

    x = {[sqrt(-1)(sqrt(y^2 +1))]/-1} + 1

    heres the steps i took if anyone get lost in that mess

    y^2 = -x^2 + 2x

    y^2 = - ( x^2 -2x)

    y^2 + 1 = -( x^2 - 2x + 1 )

    y^2 + 1 = -(x-1)^2

    (y^2 + 1)/-1 = (x-1)^2

    sqrt[ (y^2 + 1)/-1] = x-1

    {sqrt(-1)[sqrt(y^2 + 1)/-1] +1 = x
  2. 17 Jan '08 07:00
    Y^2 = 2X - X^2

    -Y^2 = x^2 - 2X

    1 - Y^2 = X^2 - 2X + 1

    1 - Y^2 = (X - 1)^2

    Sqrt (1 - Y^2) = X - 1

    1 + sqrt (1 - Y^2) = X
  3. 17 Jan '08 07:56 / 1 edit
    smomofo has it right - this is a method called "completing the square." essentially the goal is to add the same constant to both sides so as to turn the quadratic in x into a perfect square.

    ex: [some function of y] = x^2 + 4x

    add 4 to both sides: [some function of y] + 4 = x^2 +4x +4 = (x+2)^2

    now you can sqrt both sides: sqrt( [function of y] +4) = x+2

    and subtract 2, and rearrange: x = sqrt([function of y]+4) - 2

    in general, if the square you are completing is x^2 + cx then you will want to add (c/2)^2 to both sides, and the quadratic can be rewritten (x+c/2)^2.
  4. 17 Jan '08 08:03
    note: i just looked back at your algebra and noticed that your completing of the square looked ok - you seem to understand the idea.

    however, when you had y^2 = -(x^2-2x) you added 1 to the left, and added 1 to the right INSIDE the parentheses, which has a -1 coefficient. essentially, this is like adding one to the left side, and subtracting one from the right side. be careful!

    first divide both sides by -1 so the x^2 term has +1 as its coefficient, THEN add 1 to both sides. this will give you the proper 1-y^2 on the left, or possibly written, -y^2 + 1 (which is equally correct)

    good luck!