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Simple math i can't figure out

  1. Mar 18, 2010 #1
    simple math i can't figure out!!

    so i'm trying to do this chemistry problem...i have the answer, but for some reason i can't do the math myself... ive taken calculus but for some reason i just can't get this!

    i have from my answer sheet:

    (2 R)^2 + (2√2 R)^2 = (2 r + 2 R)^2

    therefore
    (√3 -1) R = r

    r/R = √3 -1 = 0.73

    ---------------------------------------------

    i cannot seem to figure out how to get to r/R ???

    when i do the math, i get

    4R^2 +8R^2= 4R^2+ 4Rr+ 4Rr+4r^2

    which i simplify to

    8R^2=8Rr+4r^2

    then to 2R^2= 2Rr+r^2

    then what?? where on earth does √3 -1 come from???

    please help!
     
  2. jcsd
  3. Mar 18, 2010 #2
    two variables, simple math that i cannot solve!

    1. The problem statement, all variables and given/known data

    I have been able to figure out this problem until I had to do some math simplification. I have the answer in front of me but i cannot seem to understand how they got to the answer that they did.

    (2 R)^2 + (2R√2)^2= (2r + 2R)^2

    therefore
    (√3 -1) R = r

    r/R = √3 -1 = 0.73

    2. Relevant equations



    3. The attempt at a solution

    I have no idea how the heck they solved for r/R to get √3 -1 = 0.73

    the furthest i can simplify the expression is down to 2R^2=2Rr+r^2

    what other steps do i need to do?! i'm desperate to figure this silly problem out!!!
     
  4. Mar 18, 2010 #3
    Re: simple math i can't figure out!!

    If you divide that by R^2, you get

    (r/R)^2 + 2 (r/R) - 2 = 0

    which is a quadratic equation for r/R with two solutions, √3 -1 and -√3 -1.

    If r and R are both positive, the second solution is unphysical.
     
  5. Mar 18, 2010 #4

    vela

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    Staff Emeritus
    Science Advisor
    Homework Helper
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    Re: two variables, simple math that i cannot solve!

    Sometimes it doesn't pay to multiply everything out and combine terms. The variable r appears in only one place in your original equation, and if that pesky 2 in the exponent wasn't there on the RHS, you could easily solve for it. To get rid of the square, you want to take the square root of both sides. So what you want to do is simplify only the left side and then take the square root of both sides of the equation.
     
  6. Mar 18, 2010 #5

    Mark44

    Staff: Mentor

    Re: two variables, simple math that i cannot solve!

    Please don't double-post your problems!
     
  7. Mar 18, 2010 #6

    berkeman

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    Staff: Mentor

    Re: simple math i can't figure out!!

    (two threads merged)
     
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