Results 1 to 7 of 7

Math Help - Real Numbers

  1. #1
    Junior Member
    Joined
    Feb 2010
    Posts
    25

    Real Numbers

    The product of 3 consecutive numbers is 1716. Find their sum.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by Drdj View Post
    The product of 3 consecutive numbers is 1716. Find their sum.
    Let the middle number be n and let the sum of them be y

    n(n-1)(n+1) = 1716

    n(n^2-1) = 1716

    n^3-n - 1716=0

    Spoiler:
    Solve the cubic. As n^3 > n you can get a rough idea by finding the cube root of 1716

    \sqrt[3] {1716} = 11.972 so guess 12.

    12^3 - 12 - 1716 = 0


    n = 12

    y = (n-1) + n + (n+1) = 3n = 36
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2010
    Posts
    25
    Thanks so much for the super-swift reply !!
    I was kinda stuck at the cubic expression, and how to do a guess-n-check properly - your cube root method was impressive indeed

    Just out of curiosity, is there a non-algebraic way to solve it ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,444
    Thanks
    1863
    I am a bit puzzled as to why you would want a "non-algebraic" way when algebra works so nicely. However, you could try this- since "three consecutive numbers" are about as close togetheras three integers can be, they must each be approximately 1716/3= 572. Try three consecutive numbers around that.

    I am wondering why you titled this "real numbers" when, to be able to talk about "consecutive" they must be integer.

    and, of course, this has nothing to do with "Statistics and Probability".
    Follow Math Help Forum on Facebook and Google+

  5. #5
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by Drdj View Post
    Thanks so much for the super-swift reply !!
    I was kinda stuck at the cubic expression, and how to do a guess-n-check properly - your cube root method was impressive indeed

    Just out of curiosity, is there a non-algebraic way to solve it ?
    I should point out that I made up that method on the spot. It won't work for small |n| though. You do get a knack for it. For example 10 would be too small
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Quote Originally Posted by HallsofIvy View Post
    I am a bit puzzled as to why you would want a "non-algebraic" way when algebra works so nicely. However, you could try this- since "three consecutive numbers" are about as close togetheras three integers can be, they must each be approximately 1716/3= 572. Try three consecutive numbers around that.

    I am wondering why you titled this "real numbers" when, to be able to talk about "consecutive" they must be integer.

    and, of course, this has nothing to do with "Statistics and Probability".
    Hi,

    But since we're talking about the product of 3 consecutive numbers, it shouldn't be 1716/3, but \sqrt[3]{1716}



    Without the cube root method, one can try to factor 1716 : /3=572, /2=286, /2=143 and 143=11*13.
    So 1716 turns out to be 11*12*13
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,444
    Thanks
    1863
    Quote Originally Posted by Moo View Post
    Hi,

    But since we're talking about the product of 3 consecutive numbers, it shouldn't be 1716/3, but \sqrt[3]{1716}



    Without the cube root method, one can try to factor 1716 : /3=572, /2=286, /2=143 and 143=11*13.
    So 1716 turns out to be 11*12*13
    I misread the problem! But your method is much nicer.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. real numbers
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: July 31st 2011, 02:59 AM
  2. Replies: 1
    Last Post: September 27th 2010, 04:14 PM
  3. Real Numbers - Real Anaylsis
    Posted in the Calculus Forum
    Replies: 5
    Last Post: September 3rd 2008, 11:54 AM
  4. real numbers
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: July 19th 2008, 01:18 AM
  5. The Sum of all real numbers
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 22nd 2005, 02:17 PM

Search Tags


/mathhelpforum @mathhelpforum