Results 1 to 4 of 4

Math Help - Make x the subject in each of the following...

  1. #1
    Senior Member
    Joined
    Jul 2009
    From
    Melbourne
    Posts
    272
    Thanks
    4

    Make x the subject in each of the following...

    I got this question but I'm not really sure how one part of the solutions came up

    tx^2+4tx+10=t

    Make x the subject in each of the following and give the values of t for which real solution(s) to the equation can be found.

    So I complete the square and get up to

    tx^2+4tx+10=t

    \frac {tx^2+4tx+10-t}{t}=0

    x^2+4x=\frac{-10}{t} +1 I moved  \frac{10}{t}-1  to the other side

     (x+2)^2 = \frac {-10}{t} +5

    (x+2)^2 = \frac {5(-2+t)}{t}

    So I just take the square root of both sides and subtract -2.

    But the solutions say x=-2 \pm\frac {\sqrt{5t(-2+t)}}{t}

    How come my answer is different...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,409
    Thanks
    1294
    \displaystyle t\,x^2 + 4t\,x + 10 = t

    \displaystyle x^2 + 4x + \frac{10}{t} = 1

    \displaystyle x^2 + 4x + 2^2 - 2^2 + \frac{10}{t} = 1

    \displaystyle \left(x + 2\right)^2 + \frac{10 - 4t}{t} = \frac{t}{t}

    \displaystyle \left(x + 2\right)^2 = \frac{5t - 10}{t}

    \displaystyle x + 2 = \pm \sqrt{\frac{5t - 10}{t}}

    \displaystyle x + 2 = \pm \sqrt{\frac{5t^2 - 10t}{t^2}}

    \displaystyle x + 2 = \pm \frac{\sqrt{5t(t - 2)}}{t}

    \displaystyle x = 2\pm \frac{\sqrt{5t(t-2)}}{t}.


    The solution the book gives (which I have posted) involves rationalising the denominator.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Jul 2009
    From
    Melbourne
    Posts
    272
    Thanks
    4
    Ahh alright, if I get a question like this in an exam or something would I have to rationalise every time? Is it wrong if I don't?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,409
    Thanks
    1294
    Quote Originally Posted by jgv115 View Post
    Ahh alright, if I get a question like this in an exam or something would I have to rationalise every time? Is it wrong if I don't?
    Both answers are correct, but it's always best to have a rational denominator.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Make Y the subject
    Posted in the Algebra Forum
    Replies: 6
    Last Post: August 17th 2011, 06:30 PM
  2. [SOLVED] Make x the subject
    Posted in the Algebra Forum
    Replies: 6
    Last Post: August 8th 2010, 07:54 AM
  3. Make t subject
    Posted in the Algebra Forum
    Replies: 30
    Last Post: December 8th 2009, 06:52 AM
  4. make L subject
    Posted in the Algebra Forum
    Replies: 3
    Last Post: November 29th 2009, 02:54 PM
  5. make y the subject...
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: November 1st 2008, 02:23 PM

/mathhelpforum @mathhelpforum