Results 1 to 7 of 7
Like Tree3Thanks
  • 2 Post By veileen
  • 1 Post By veileen

Math Help - Problem with solving an equation

  1. #1
    Newbie
    Joined
    Feb 2013
    From
    Stockholm
    Posts
    4

    Problem with solving an equation

    I am stuck with this equation and would be glad if someone could help me out.
    So please help me with how to solve this equation.

    (x-5)/((x+1)^(1/2))=(-x^2+7*x-10)/((x^2-x-2)^(1/2))

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Mar 2011
    From
    Awetuouncsygg
    Posts
    182
    Thanks
    12

    Re: Problem with solving an equation

    First things first:

    x+1> 0\Rightarrow x > -1

    x^2-x-2>0\Rightarrow (x+1)(x-2)>0\Rightarrow x\in (-\infty , -1) \cup (2, \infty)

    So our x is strictly bigger than 2.

    \frac{x-5}{\sqrt{x+1}}=\frac{-x^2+7x-10}{\sqrt{x^2-x-2}} \Leftrightarrow \frac{x-5}{\sqrt{x+1}}=\frac{-(x-2)(x-5)}{\sqrt{(x+1)(x-2)}}

    If x = 5, we obtain 0 = 0 which is true, so 5 is one of the solutions.

    If x \neq 5:

    \frac{x-5}{\sqrt{x+1}}=\frac{-(x-2)(x-5)}{\sqrt{(x+1)(x-2)}}\Leftrightarrow

    \frac{x-5}{\sqrt{x+1}}=\frac{(x-5)}{\sqrt{x+1}}\cdot \frac{-(x-2)}{\sqrt{x-2}}

    \Leftrightarrow \frac{-(x-2)}{\sqrt{x-2}}=1\Leftrightarrow -\sqrt{x-2}=1 Impossible.

    So x = 5 is the only solution.
    Thanks from Paze and Zhirkov
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member Paze's Avatar
    Joined
    Nov 2012
    From
    Iceland
    Posts
    379
    Thanks
    19

    Re: Problem with solving an equation

    Hi Zhirkov.

    You have the equation: \frac{x-5}{\left({x+1}\right)^{1/2}}=\frac{-x^2+7x-10}{\left({x^2-x-2}\right)^{1/2}}?

    Because it is an unnecessary long computation as far as I know.

    EDIT: Never mind, I see you have received an answer above.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Feb 2013
    From
    Stockholm
    Posts
    4

    Re: Problem with solving an equation

    Thank you for your help!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Feb 2013
    From
    Stockholm
    Posts
    4

    Re: Problem with solving an equation

    A couple of question though if it is okay. How do go from the second last step to the last one and what do you mean with impossible? You can still solve the last step of the equation and get a value of X out of that. And is it possible to just compute the equation until you get x=5?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Mar 2011
    From
    Awetuouncsygg
    Posts
    182
    Thanks
    12

    Re: Problem with solving an equation

    You're welcome! ^^

    Quote Originally Posted by Zhirkov View Post
    A couple of question though if it is okay. How do go from the second last step to the last one and what do you mean with impossible? You can still solve the last step of the equation and get a value of X out of that. And is it possible to just compute the equation until you get x=5?
    Starting from here:

    \frac{x-5}{\sqrt{x+1}}=\frac{(x-5)}{\sqrt{x+1}}\cdot \frac{-(x-2)}{\sqrt{x-2}}

    I multiplied the relation with \frac{\sqrt{x+1}}{x-5} \neq  0 and obtained:

    1=\frac{-(x-2)}{\sqrt{x-2}} \Leftrightarrow 1=\frac{-(\sqrt{x-2})^2}{\sqrt{x-2}} \Leftrightarrow 1=-\sqrt{x-2}


    -\sqrt{x-2}=1 is impossible because \sqrt{x-2}>0 \Rightarrow -\sqrt{x-2}<0 and 1 > 0.
    Thanks from Zhirkov
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Feb 2013
    From
    fghgj
    Posts
    4

    Re: Problem with solving an equation

    Thank you for your help!

    _________________
    Wacth the dvd movies online with exquisite dvd user and have the best price!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Problem with solving equation
    Posted in the Calculus Forum
    Replies: 6
    Last Post: September 1st 2011, 08:04 AM
  2. problem in solving equation..
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: May 1st 2010, 04:35 AM
  3. simultaneous equation problem solving
    Posted in the Algebra Forum
    Replies: 4
    Last Post: February 11th 2010, 02:42 AM
  4. Problem solving a simple equation- Help!
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 7th 2007, 08:29 PM
  5. solving this equation problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: December 3rd 2005, 10:40 PM

Search Tags


/mathhelpforum @mathhelpforum