Results 1 to 5 of 5

Math Help - How are these equal? Last question.

  1. #1
    Member
    Joined
    Aug 2008
    Posts
    218

    How are these equal? Last question.

    Show that  (2^\frac{1}{3})^{-2} +2^\frac{1}{3} -2 = \frac{3*2^\frac{1}{3}}{2} - 2.


    I usually use my calculator to convert from one form to another, but I don't actually see or understand how it is really the same. Any help would be appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Mollier's Avatar
    Joined
    Nov 2009
    From
    Norway
    Posts
    234
    Awards
    1
    Hi, I will show you one way of doing this.

    I multiply the whole thing by 2,

    2^{-2/3}\cdot 2^1 + 2^{1/3}\cdot 2^1 - 2^2 = 3\cdot 2^{1/3} - 2^2

    Then by using the fact that 2 2^a\cdot 2^b = 2^{a+b} we get,

    2^{1/3} + 2^{4/3} = 3\cdot 2^{1/3}

    Finally we get,

    2^{4/3} = 2^{1/3}(3-1),

    and I hope the rest is clear.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,201
    Thanks
    1789
    Another way to do it:
    (2^\frac{1}{3})^{-2} +2^\frac{1}{3}= 2^{-2/3}+ 2^{1/3}= \left(2^{1/3}\right)\left(2^{-3/3}+ 1\right) = \left(2^{1/3}\right)\left(\frac{1}{2}+ 1\right)= \left(2^{1/3}\right)\left(\frac{3}{2}\right). Now subtract 2 from both sides.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,859
    Thanks
    741
    Hello, Joker37!

    I went at it head-on . . . no fancy tricks.


    Show that: .  (2^\frac{1}{3})^{-2} +2^\frac{1}{3} -2 \;=\; \dfrac{3\cdot2^\frac{1}{3}}{2} - 2

    (2^{\frac{1}{3}})^{-2} + 2^\frac{1}{3}} - 2 \;\;=\;\;2^{-\frac{2}{3}} + 2^{\frac{1}{3}}} - 2

    . . . . \displaystyle =\;\;\dfrac{1}{2^{\frac{2}{3}}} + 2^{\frac{1}{3}} - 2 \;\;=\;\;\frac{1}{2^{\frac{2}{3}}}\cdot\frac{2^{\f  rac{1}{3}}}{2^{\frac{1}{3}}}  + 2^{\frac{1}{3}}\cdot\frac{2}{2} - 2

    . . . . \displaystyle =\;\; \frac{2^{\frac{1}{3}}}{2} + \frac{2\cdot2^{\frac{1}{3}}}{2} - 2 \;\;=\;\;\frac{3\cdot2^{\frac{1}{3}}}{2} - 2

    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,113
    Thanks
    68
    You can also manipulate such that you get 3 / 2^(2/3) ; try it.

    Curious: why in heck have "-2" on each side ?!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Equal power sets -> Equal sets?
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: July 5th 2012, 10:23 AM
  2. Difficult Geometry Question - Equal Intervals
    Posted in the Geometry Forum
    Replies: 3
    Last Post: March 26th 2011, 02:33 AM
  3. [SOLVED] Is it really equal? Why?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 7th 2010, 12:51 PM
  4. Question on > or equal symbol
    Posted in the Algebra Forum
    Replies: 1
    Last Post: July 2nd 2010, 01:00 PM
  5. Replies: 2
    Last Post: March 23rd 2009, 08:11 AM

Search Tags


/mathhelpforum @mathhelpforum