Results 1 to 9 of 9

Math Help - formulas...

  1. #1
    Junior Member
    Joined
    Oct 2005
    Posts
    37

    Post formulas...

    given :a+b=8 ab=12

    how much is:
    a-b
    a^2+b^2

    1 + 1
    a^2 b^2


    Thanks! I need it for a test tomorrow so please help me fast
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by dgolverk
    given :a+b=8 ab=12

    how much is:
    a-b
    a^2+b^2

    1 + 1
    a^2 b^2


    Thanks! I need it for a test tomorrow so please help me fast
    Just by looking, (a or b) = 2, and (a or b) = 6.

    Let us use some Math.
    Here is one way.

    a +b = 8 ----(i)
    ab = 12 -----(ii)
    From (ii), a = 12/b
    Substitute that into (i),
    12/b +b = 8
    Clear the fraction, multiply both sides by b,
    12 +b^2 = 8b
    b^2 -8b +12 = 0
    (b-2)(b-6) = 0

    b-2 = 0
    b = 2

    b-6 = 0
    b = 6

    So, b = 2 or 6 --------***
    Then, a = 12/b = 6 or 2 ----------***
    Hence, we have two sets of answers:
    a=2, and b=6 -----(1)
    a=6, and b=2 -----(2)

    -----------------------------------------------
    When a=2 and b=6:

    a -b = 2 -6 = -4 -----------------------------answer.
    a^2 +b^2 = 2^2 +6^2 = 4 +36 = 40 ---------answer.

    1/(a^2) +1/(b^2)
    = 1/(2^2) +1/(6^2)
    = 1/4 +1/36
    = (9 +1)/36
    = 10/36
    = 5/18 ------------------answer.

    --------------------------------------------------
    When a=6 and b=2:

    a -b = 6 -2 = 4 -----------------------------answer.
    a^2 +b^2 = 6^2 +2^2 = 36 +4 = 40 ---------answer.

    1/(a^2) +1/(b^2)
    = 1/(6^2) +1/(2^2)
    = 1/36 +1/4
    = (1 +9)/36
    = 10/36
    = 5/18 ------------------answer.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2005
    Posts
    37

    Thanks

    but...
    I forgot to notice that you shouldn't find how much is a or b.
    you should find how much is a-b etc... togther...
    I very appreciate your help.
    by the way...
    You need use in these formulas:
    (a+b)^2
    (a-b)^2
    (a-b)(a+b)
    Last edited by dgolverk; January 28th 2006 at 04:52 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by dgolverk
    given :a+b=8 ab=12

    how much is:
    a-b
    a^2+b^2

    1 + 1
    a^2 b^2


    Thanks! I need it for a test tomorrow so please help me fast
    Start with:

    (a+b)^2=a^2+b^2+2ab,

    so:

    a^2+b^2=(a+b)^2-2ab=64-24=40.

    Now:

    (a-b)^2=a^2+b^2-2ab=40-24=16

    so:

    a-b=\pm 4,

    we can leave the \pm here as the information we have been
    given is symmetric in a and b and so this sign
    ambiguity remains.

    Now:

    \frac{1}{a^2}+\frac{1}{b^2}=\frac{a^2+b^2}{a^2b^2}  =\frac{a^2+b^2}{(ab)^2}=\frac{40}{144}=\frac{5}{18  }.

    RonL
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Oct 2005
    Posts
    37

    Thanks a lot!

    but now i have another problem...
    given:
    a+b=7

    a-b=5

    find how much is:
    a^2+b^2

    ab

    Thanks again
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by dgolverk
    but...
    I forgot to notice that you shouldn't find how much is a or b.
    you should find how much is a-b etc... togther...
    I very appreciate your help.
    by the way...
    You need use in these formulas:
    (a+b)^2
    (a-b)^2
    (a-b)(a+b)
    Is that so? So no going to find the values of a and b?
    Okay.

    Here is one way of doing that,

    a+b = 8 ----(i)
    ab = 12 --------(ii)
    Find 1) a-b; 2) a^2 +b^2; and 3) 1/(a^2) +1/(b^2) without solving for the values of a and b.

    ----------------
    The a^2 +b^2 first.

    (a+b)^2 = 8^2 = 64
    but (a+b)^2 = a^2 +2ab +b^2 also, so,
    Substituting 12 for ab, and 64 for (a+b)^2,
    64 = a^2 +2(12) +b^2
    64 -24 = a^2 +b^2
    40 = a^2 +b^2
    Or,
    a^2 +b^2 = 40 ---------answer.

    -----------------------------------------
    The a-b.

    (a-b)^2 = a^2 -2ab +b^2
    (a-b)^2 = (a^2 +b^2) -2ab
    Substitutions,
    (a-b)^2 = 40 -2(12)
    (a-b)^2 = 16
    Take the square roots of both sides,
    a-b = +,-4 ----------------------------answer.
    That is "plus or minus" 4.

    ---------------------------------------------
    The 1/(a^2) + 1/(b^2).

    1/(a^2) +1/(b^2)
    Combine the two fractions into one fraction only,
    = [(b^2)*1 +(a^2)*1] / [(a^2)(b^2)]
    = [a^2 +b^2] / [(ab)^2]
    Substitutions,
    = [40] / [(12)^2]
    = 40 / 144
    Reduce to lowest term, divide numerator and denominator by 8,
    = 5/18 ---------answer.

    -----------------------------------------
    Do the answers here tally with the answers in my first answer where I solved for and b first?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by dgolverk
    but now i have another problem...
    given:
    a+b=7

    a-b=5

    find how much is:
    a^2+b^2

    ab

    Thanks again
    Easy-Peasy:

    (a+b)^2=a^2+b^2+2ab=49
    (a-b)^2=a^2+b^2-2ab=25

    So adding these gives:

    (a^2+b^2+2ab)+(a^2+b^2-2ab)=49+25=74,

    but simplifying the LHS this is:

    2(a^2+b^2)=74,

    so:

    a^2+b^2=37.

    Subtracting the same two equations as before were added gives:

    4ab=49-25=24

    so:

    ab=6.

    RonL
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Oct 2005
    Posts
    37

    Thanks!

    You really helped me!
    Thanks again!
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by dgolverk
    but now i have another problem...
    given:
    a+b=7

    a-b=5

    find how much is:
    a^2+b^2

    ab

    Thanks again
    Umm, you're too young yet and you have many problems already?

    (a+b)^2 = a^2 +2ab +b^2 = 7^2 = 49 ----(1)
    (a-b)^2 = a^2 -2ab +b^2 = 5^2 = 25 --------(2)

    Add (1) and (2),
    2(a^2 +b^2) = 74
    So,
    a^2 +b^2 = 37 -----answer.

    Substitute that into, say, (a-b)^2,
    (a-b)^2 = a^2 -2ab +b^2
    Substitutions,
    (5)^2 = 37 -2ab
    25 -37 = -2ab
    -12 = -2ab
    So,
    ab = 6 ------------answer.

    -----------------------------------------
    Zeez, I posted my replies late. I need to rev this one-finger typer of mine. Steroids, maybe.
    But gotta get some sleep first. 'Night.
    Last edited by ticbol; January 28th 2006 at 05:54 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help with formulas?
    Posted in the Algebra Forum
    Replies: 6
    Last Post: September 30th 2009, 07:12 PM
  2. I need formulas.....
    Posted in the Business Math Forum
    Replies: 7
    Last Post: August 24th 2009, 04:06 PM
  3. formulas help
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 20th 2008, 03:39 PM
  4. Using sin,cos,tan formulas.
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: March 15th 2007, 02:03 PM
  5. Formulas
    Posted in the Algebra Forum
    Replies: 3
    Last Post: April 28th 2005, 08:02 AM

Search Tags


/mathhelpforum @mathhelpforum