Results 1 to 2 of 2

Thread: Express the following by using 't'

  1. #1
    Newbie
    Joined
    Jan 2010
    From
    Goyang, South Korea
    Posts
    4

    Express the following by using 't'

    When

    $\displaystyle t=\frac{{a^{2}+b^{2}}}{{a^{2}-b^{2}}}+
    \frac{{a^{2}-b^{2}}}{{a^{2}+b^{2}}}$

    express the following by using 't'

    $\displaystyle \frac{{a^{8}+b^{8}}}{{a^{8}-b^{8}}}+
    \frac{{a^{8}-b^{8}}}{{a^{8}+b^{8}}}$

    -----------------------------------------------------

    So,, I got this problem and the first thing I did was factoring
    and I found the common denominator of 't'

    Then it turned out that

    $\displaystyle t=\frac{{2(a^{4}+b^{4})}}{{a^{4}-b^{4}}}$

    Also I could change 'the follwing' into this.

    $\displaystyle \frac{{2(a^{16}+b^{16})}}{{a^{16}-b^{16}}}$

    Next, I tried dividing 'the following' by 't' so that I can find out what I should multiply to 't' to make it as 'the following'.

    $\displaystyle \frac{{(a^{16}+b^{16})}({a^{4}-b^{4})}}{({a^{16}-b^{16})}({a^{4}+b^{4})}}$


    .... And now I'm stuck.
    I felt like I was getting closer to the answer but....

    Any help would be appreciated..
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    We have $\displaystyle t=\frac{2(a^4+b^4)}{a^4-b^4}$

    $\displaystyle a^4t-b^4t=2a^4+2b^4\Rightarrow\left(\frac{a}{b}\right)^ 4=\frac{t-2}{t+2}\Rightarrow\left(\frac{a}{b}\right)^8=\left (\frac{t-2}{t+2}\right)^2$.

    Now, $\displaystyle \frac{a^8+b^8}{a^8-b^8}+\frac{a^8-b^8}{a^8+b^8}=\frac{\left(\frac{a}{b}\right)^8+1}{ \left(\frac{a}{b}\right)^8-1}+\frac{\left(\frac{a}{b}\right)^8-1}{\left(\frac{a}{b}\right)^8+1}$

    Replace $\displaystyle \left(\frac{a}{b}\right)^8$ with $\displaystyle \left(\frac{t-2}{t+2}\right)^2$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Express 2x^2-28x+53
    Posted in the Algebra Forum
    Replies: 7
    Last Post: May 16th 2011, 05:27 AM
  2. Different way to express this set
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: Feb 21st 2011, 11:46 AM
  3. express in m and n
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: Jul 22nd 2010, 09:15 PM
  4. express in z=a+bi
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Apr 14th 2009, 11:52 PM
  5. way to express ans
    Posted in the Trigonometry Forum
    Replies: 8
    Last Post: Apr 17th 2006, 07:00 AM

Search Tags


/mathhelpforum @mathhelpforum