Results 1 to 6 of 6

Math Help - 4x^2-1/4x^2

  1. #1
    Junior Member
    Joined
    Oct 2007
    Posts
    55

    4x^2-1/4x^2

    4x^2-1/4x^2

    its supposed to equal 15/16ths somehow?Or atleast thats what my teacher told me. Could you show me how this equals 15/16ths?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Jun 2007
    Posts
    65
    Ok well we see that 4x^2 = 16 from the bottom so now let's solve for x

    4x^{2}=16
    x^{2}=4
    x =\sqrt{4}
    So we get  x = \pm 2
    (Remember that square roots always have 2 roots)
    Now we can see if it satisfies the numerator.
    4(2)^2-1 = 15
    4(4)-1 = 15
    16 - 1 = 15
    and of course  15 = 15

    So we found that  x = \pm 2
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,184
    Thanks
    403
    Awards
    1
    Quote Originally Posted by bilbobaggins View Post
    4x^2-1/4x^2

    its supposed to equal 15/16ths somehow?Or atleast thats what my teacher told me. Could you show me how this equals 15/16ths?
    SnipedYou:
    You can in this particular instance assume that the numerator is 15 and the denominator is 16, but you first have to show that 4x^2 - 1 and 4x^2 are relatively prime, a problem that I doubt bilbobaggins is going to want to do.

    Here's the general method:
    \frac{4x^2 - 1}{4x^2} = \frac{15}{16}

    16(4x^2 - 1) = 15(4x^2)

    64x^2 - 16 = 60x^2

    4x^2 = 16

    x^2 = 4

    Thus
    x = \pm 2

    -Dan
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member DivideBy0's Avatar
    Joined
    Mar 2007
    From
    Melbourne, Australia
    Posts
    432
    I wonder if he means \frac{4x^2-1}{4x^2}=\frac{15}{16} for all x?

    Well that is false. It cannot simplify down to \frac{15}{16}.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jun 2007
    Posts
    65
    Is there a case where 2 consecutive numbers aren't relatively prime?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,184
    Thanks
    403
    Awards
    1
    Quote Originally Posted by SnipedYou View Post
    Is there a case where 2 consecutive numbers aren't relatively prime?
    No, but I suspect if bilbobaggins didn't know how to solve the problem the long way (my way) I doubt he would have even considered the concept of relatively prime in solving this.

    -Dan
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum