Results 1 to 5 of 5

Math Help - Easiest way to solve

  1. #1
    Junior Member
    Joined
    Jul 2009
    Posts
    59

    Easiest way to solve

    What is the simplest way to solve this problem?

    |x+1|^2+3|x+1|-4=0
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,548
    Thanks
    539
    Hello, Mike9182!

    What is the simplest way to solve this equation?

    . . |x+1|^2+3|x+1|-4\:=\:0
    We have a quadratic . . . Solve it accordingly.


    Factor: . \left(|x+1| + 4\right)\left(|x+1| - 1\right) \:=\:0


    Set each factor equal to zero and solve:

    . . |x+1| + 4 \:=\:0 \quad\Rightarrow\quad|x+1| \:=\:-4 . . . no roots
    . . . .
    An absolute value is never negative.

    . . |x+1| - 1 \:=\:0 \quad\Rightarrow\quad |x+1| \:=\:1 \quad\Rightarrow\quad x+1 \:=\:\pm1 \quad\Rightarrow\quad x \:=\:0,\:2


    But x=2 is extraneous.

    . . Therefore, the only solution is: . x \:=\:0

    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570

    Absolute value

    Hello Mike9182
    Quote Originally Posted by Mike9182 View Post
    What is the simplest way to solve this problem?

    |x+1|^2+3|x+1|-4=0
    Let y = |x+1|. Then:

    y^2 +3y - 4=0

    \Rightarrow (y+4)(y-1)=0

    \Rightarrow y=-4, \,1

    But y = -4 is impossible, since |x+1| \ge 0

    \Rightarrow y =1= |x+1|

    \Rightarrow x+1 = \pm 1

    \Rightarrow x = 0,\, -2

    Grandad
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7
    Quote Originally Posted by Soroban View Post
    x+1 \:=\:\pm1 \quad\Rightarrow\quad x \:=\:0,\:2
    Am I missing something?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by alexmahone View Post
    Am I missing something?
    probably just a typo ... it happens.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Easiest way to solve
    Posted in the Algebra Forum
    Replies: 1
    Last Post: April 18th 2011, 03:36 PM
  2. Easiest way to solve
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: September 3rd 2009, 01:16 AM
  3. Probability at its easiest!
    Posted in the Statistics Forum
    Replies: 2
    Last Post: August 8th 2009, 02:34 PM
  4. Easiest Sum for You'll
    Posted in the Geometry Forum
    Replies: 3
    Last Post: July 7th 2008, 08:30 PM
  5. What is the EASIEST way to solve this?
    Posted in the Algebra Forum
    Replies: 5
    Last Post: April 23rd 2006, 01:24 PM

Search Tags


/mathhelpforum @mathhelpforum