Math problem - solving for a variable

  1. 1. The problem statement, all variables and given/known data

    sqrt(2x+4) = sqrt(6x+1) - 1

    I Need to solve for x, but cannot seem to get the same answer as the text. (Ans. x= 5/2)

    3. The attempt at a solution

    sqrt(2x+4) - sqrt(6x+1) = -1
    square both sides
    (2x+4) - (6x+1) = 1
    -4x-3=1
    -4x=4
    x=-1 ??

    I know I must be doing something wrong, it has been a while since I have done this sort of problem.

    Thank you for your time.
     
  2. jcsd
  3. vela

    vela 12,632
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Your mistake is in thinking (a-b)2 = a2-b2, which is what you did when you squared the lefthand side of the equation. You need to multiply it out correctly.
     
  4. Im still not there yet:

    My new attempt:

    [​IMG]

    I cant seem to get rid of the sqrt (x)
    i know sqrt(12x) = 2*sqrt(3x)
     
  5. vela

    vela 12,632
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Now you're making even more mistakes. First,

    [sqrt(2x+4)-sqrt(6x+1)]2 ≠ (2x+4) - (6x+1)

    Second,

    sqrt(a+b) ≠ sqrt(a)+sqrt(b)

    which is what you're doing going from the fifth line to the sixth line. You were, however, correct when you said earlier that

    (sqrt(2x+4))2 = 2x+4



    The problem is actually a bit easier to solve if you square both sides right away:

    (sqrt(2x+4))2 = (sqrt(6x+1)-1)2

    To correctly calculate the righthand side, let a=sqrt(6x+1) and b=1. Then your equation becomes

    (sqrt(2x+4))2 = (a-b)2

    Now FOIL out the righthand side and then substitute back in for a and b.
     
    Last edited: Aug 13, 2010
  6. Im sorry, I am unable to see that. All i can see is black and faint white portions. Is it possible for you to take a screen shot and upload to image shack?
     
  7. vela

    vela 12,632
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    I edited my previous post and took out the images. You should be able to read it now.
     
  8. I got it, thank you for your help.
    It took a while to come back to me. I appreciate your time, thank you.

    [​IMG]
     
  9. Mark44

    Staff: Mentor

    Looks fine.
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?
Similar discussions for: Math problem - solving for a variable
Loading...