Results 1 to 7 of 7

Math Help - Inequalities with radicals problem?

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    1

    Inequalities with radicals problem?

    How should i solve this?

    √x^2-9>x+6
    so x^2-9<0
    x<3

    Im supposed to find all the possible roots or whatever and im not sure what that means/how to do it or if im even doing this problem right
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,910
    Thanks
    1760
    Awards
    1
    Quote Originally Posted by lizzytish881 View Post
    How should i solve this?

    √x^2-9>x+6
    so x^2-9<0
    x<3

    Im supposed to find all the possible roots or whatever and im not sure what that means/how to do it or if im even doing this problem right
    Do you understand that your posting is next to impossible to read?
    Why not learn to post in symbols? You can use LaTeX tags.
    [tex]\sqrt{x^2+1}[/tex] gives  \sqrt{x^2+1} .
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,115
    Thanks
    68
    Can you solve this: SQRT(x^2 - 9) = x + 6
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Mar 2010
    Posts
    48
    Quote Originally Posted by Wilmer View Post
    Can you solve this: SQRT(x^2 - 9) = x + 6
    I'll give you the first step. Square both sides. Then you have

    {x}^{2}-9= \left( x+6 \right) ^{2}

    Now you must expand the right side. Use the FOIL method (First, outer, inner, last).
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,115
    Thanks
    68
    Arcketer, my post was addressed to the original poster...
    to see if able to solve as a NON-equality...get it?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,208
    Thanks
    1789
    Yes, I suspect he understood that. The best way to solve a complicated inequality is to first solve the associated equation.

    Square both sides of \sqrt{x^2- 9}= x- 6 to get x^2- 18x+ 81= x^2- 12x+ 36. Solve that for x. That divides the real numbers into two intervals. Check one value of x in each interval to see if it satisfies the inequality. If it does, then every point in the interval satisfies the inequality.

    Also, in order that the square root be real, you must x^2- 9> 0. Again, the best way to solve that is to first solve the equation.
    x^2- 9= 0 for x= 3 and x= -3. Checking one point of x< -3, -3< x< 3, and x> 3, we see that x< -3 and x> 3 satisfy x^2- 9> 0. The point in the interval above such that either of those is true satisfy the original inequality.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    Spoiler:

    the case x\le-6 is trivial and we easily see that the inequality holds.

    in order to square both sides, we require that x\ge-6 as long as the radicand is well defined, putting that together we require x\in[-6,-3].

    square and get x<-\frac{15}4, thus the second solution set is x\in \left[ -6,-\frac{15}{4} \right[ and the final solution set is \left] -\infty ,-6 \right]\cup \left[ -6,-\frac{15}{4} \right[=\left] -\infty ,-\frac{15}{4} \right[.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. limit problem with radicals
    Posted in the Calculus Forum
    Replies: 7
    Last Post: June 12th 2009, 01:07 AM
  2. Simplifying Radicals and Exponents Problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 30th 2008, 08:13 PM
  3. Solving inequalities with radicals
    Posted in the Algebra Forum
    Replies: 4
    Last Post: December 31st 2007, 09:47 AM
  4. Radicals Problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 22nd 2007, 02:01 PM
  5. Another confusing radicals problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 21st 2007, 09:32 PM

Search Tags


/mathhelpforum @mathhelpforum