Results 1 to 4 of 4
Like Tree1Thanks
  • 1 Post By Prove It

Math Help - PROVING an INEQUALITY

  1. #1
    Junior Member Kaloda's Avatar
    Joined
    Sep 2010
    Posts
    74

    PROVING an INEQUALITY

    If x is any real number, then prove that x^2+2x+4\geq0.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,318
    Thanks
    1234

    Re: PROVING an INEQUALITY

    Quote Originally Posted by Kaloda View Post
    If x is any real number, then prove that x^2+2x+4\geq0.
    \displaystyle \begin{align*} x^2 + 2x + 4 &= x^2 + 2x + 1^2 - 1^2 + 4 \\ &= (x + 1)^2 + 3 \\ &\geq 0 \end{align*}
    Thanks from Kaloda
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member Kaloda's Avatar
    Joined
    Sep 2010
    Posts
    74

    Re: PROVING an INEQUALITY

    Hahahahahahahaha! Now I know how dumb I am. Btw, thanks.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,279
    Thanks
    670

    Re: PROVING an INEQUALITY

    alternatively, you could look at the discriminant: b2 - 4ac of the quadratic x2+2x + 4, which is:

    4 - 4(1)(4) = -12 < 0.

    this tells you that the parabola:

    y = x2+2x + 4 never crosses the x-axis, and since it "opens up" (the x2 term is positive), it must lie entirely above the x-axis

    (not only is the inequality true, but we can also replace "≥" with ">". in fact, the value of x2+2x + 4 never gets smaller than 3, which happens at x = -1).
    Last edited by Deveno; August 12th 2012 at 09:37 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. proving an inequality
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 6th 2011, 02:44 PM
  2. Replies: 3
    Last Post: December 12th 2010, 01:16 PM
  3. Help with proving an inequality
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 9th 2009, 12:34 PM
  4. Proving inequality
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 16th 2009, 08:03 AM
  5. Proving an Inequality
    Posted in the Algebra Forum
    Replies: 3
    Last Post: September 4th 2008, 12:58 PM

Search Tags


/mathhelpforum @mathhelpforum