Results 1 to 3 of 3

Thread: Equations Reducible To Quadratics

  1. #1
    Senior Member
    Joined
    Jul 2008
    Posts
    347

    Equations Reducible To Quadratics

    For x^4 - 8x^2-4= 0 ,

    Does x work out to be = +/-√(4+/-2√5)

    N.B. +/- means + or -

    I've subbed in my answer but it doesnt seem to work. I've tried finding x using quadratic formula and completing the square.

    Can anyone please help?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Aug 2008
    Posts
    80
    Hello,

    I think you are doing the right thing. Just one word: since $\displaystyle 4-2\sqrt{5}<0$, $\displaystyle \pm\sqrt{4-2\sqrt{5}}$ are imaginary numbers.

    Bye.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    12,880
    Thanks
    1946
    Quote Originally Posted by xwrathbringerx View Post
    For x^4 - 8x^2-4= 0 ,

    Does x work out to be = +/-√(4+/-2√5)

    N.B. +/- means + or -

    I've subbed in my answer but it doesnt seem to work. I've tried finding x using quadratic formula and completing the square.

    Can anyone please help?
    Here's how it's solved...

    $\displaystyle x^4 - 8x^2 - 4 = 0$.

    Let $\displaystyle X = x^2$.

    So we have $\displaystyle X^2 - 8X - 4 = 0$.

    Using the Quadratic formula $\displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ we find

    $\displaystyle X = \frac{8 \pm \sqrt{64 + 16}}{2} = \frac{8 \pm \sqrt{80}}{2}$

    $\displaystyle = \frac{8 \pm 4\sqrt{5}}{2} = 4 + 2\sqrt{5}$ or $\displaystyle 4 - 2\sqrt{5}$.


    Since $\displaystyle x^2 = X$ we have

    $\displaystyle x^2 = 4 + 2\sqrt{5}$ or $\displaystyle x^2 = 4 - 2\sqrt{5}$.


    So $\displaystyle x = \pm \sqrt{4 \pm 2\sqrt{5}}$.

    So yes, you're right.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Reducible Equations
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: Jul 14th 2010, 03:56 AM
  2. Replies: 4
    Last Post: Dec 7th 2008, 12:52 AM
  3. Quadratics and simultaneous equations
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Sep 7th 2008, 02:49 AM
  4. Quadratics and simultaneous equations
    Posted in the Algebra Forum
    Replies: 8
    Last Post: Sep 6th 2008, 01:51 PM
  5. Two Quadratics Equations
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Jul 26th 2007, 03:58 AM

Search Tags


/mathhelpforum @mathhelpforum