Results 1 to 7 of 7

Math Help - Simplification 2

  1. #1
    Member
    Joined
    Jan 2011
    Posts
    95

    Simplification 2

    Hi All,

    [tex]{3}^{x} = {3}^{-x} = \sqrt{b+1}[\MATH]

    Simplifies to [tex]{3}^{2x} + 2.3^{x}.3^{-x} + 3^{-2x} = b + 2[\MATH]

    but how do we get .. 2.3^{x}.3^{-x} in the above? Would it not just be {3}^{2x} + 3^{-2x} = b +2?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    10,969
    Thanks
    1011
    You clearly have a typo, since there are three equalities in your first line...

    Assuming that's actually 3^x + 3^{-x} = \sqrt{b + 1}

    (3^x + 3^{-x})^2 = (\sqrt{b + 1})^2

    3^{2x} + 2(3^x)(3^{-x}) + 3^{-2x} = b + 1

    3^{2x} + 2(1) + 3^{-2x} = b + 1

    3^{2x} + 3^{-2x} = b - 1

    So the simplification you are given is also incorrect.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,547
    Thanks
    539
    Hello, dumluck!

    . . . . . . . . . . . . . . . . . _____
    3^{x} + 3^{-x} .= .√b + 1

    Simplifies to: .3^{2x} + 2*3^{x}*3^{-x} + 3^{-2x} .= .b + 1

    but how do we get: .2*3^{x}*3^{-x} in the above?

    Would it not just be: .3^{2x} + 3^{-2x} .= .b +1 ? . certainly not!

    Hey, you know better! . (a + b)^2 . .a^2 + b^2

    Fact: .(a + b)^2 .= .a^2 + 2ab + b^2

    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    10,969
    Thanks
    1011
    Quote Originally Posted by Soroban View Post
    Hello, dumluck!


    Hey, you know better! . (a + b)^2 . .a^2 + b^2

    Fact: .(a + b)^2 .= .a^2 + 2ab + b^2

    Actually (a + b)^2 = a^2 + b^2 if and only if a = 0 or b = 0...
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Jan 2011
    Posts
    95
    Quote Originally Posted by Soroban View Post
    Hello, dumluck!


    Hey, you know better! . (a + b)^2 . .a^2 + b^2

    Fact: .(a + b)^2 .= .a^2 + 2ab + b^2

    Ah yes, so in the example above (3^x + 3^{-x})^2


    It would be (3^x + 3^-x)(3^x + 3^-x)

    So (3^x)(3^x) + (3^x)(3^-x) + (3^-x)(3^x) + (3^-x)(3^-x)

    and as prove it denoted this translates to.

    3^{2x} + 2(3^x)(3^{-x}) + 3^{-2x}

    3^{2x} + 2(1) + 3^{-2x} = b + 1 :

    Where did the two disappear too, and why has the sign of the 1 changed in the next step?

    3^{2x} + 3^{-2x} = b - 1

    thx.






    ?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,668
    Thanks
    298
    Awards
    1
    Quote Originally Posted by dumluck View Post
    Ah yes, so in the example above (3^x + 3^{-x})^2


    It would be (3^x + 3^-x)(3^x + 3^-x)

    So (3^x)(3^x) + (3^x)(3^-x) + (3^-x)(3^x) + (3^-x)(3^-x)

    and as prove it denoted this translates to.

    3^{2x} + 2(3^x)(3^{-x}) + 3^{-2x}

    3^{2x} + 2(1) + 3^{-2x} = b + 1 :

    Where did the two disappear too, and why has the sign of the 1 changed in the next step?

    3^{2x} + 3^{-2x} = b - 1

    thx.






    ?
    3^{2x} + 2(1) + 3^{-2x} = b + 1

    3^{2x} + 2(1) + 3^{-2x} - 2 = b + 1 - 2

    3^{2x} + 3^{-2x} = b - 1

    -Dan
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Jan 2011
    Posts
    95
    Quote Originally Posted by topsquark View Post
    3^{2x} + 2(1) + 3^{-2x} = b + 1

    3^{2x} + 2(1) + 3^{-2x} - 2 = b + 1 - 2

    3^{2x} + 3^{-2x} = b - 1

    -Dan
    of course.. thanks.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simplification
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 1st 2010, 05:52 AM
  2. Simplification
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 16th 2009, 02:20 PM
  3. Exp of Log simplification
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 30th 2008, 11:59 AM
  4. Simplification
    Posted in the Algebra Forum
    Replies: 3
    Last Post: April 29th 2008, 05:14 AM
  5. Simplification
    Posted in the Algebra Forum
    Replies: 1
    Last Post: April 3rd 2008, 11:04 PM

Search Tags


/mathhelpforum @mathhelpforum