Last one of the day I promise.

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1 over 2 sqrt 3+1 = 2 sqrt 3-1 over 11 true or false?

I have gotten MUCH better at this stuff honestly I am only posting a few of the problems that I have been doing. We have over 50 pages a week in the text, plus 30 or so homework problems, he gives us brain teasers, discussion questions and tests. So, I am getting there slowly.

We have nothing in the book showing me how to proceed with this. Could you steer me in the right direction?
 
There are several ways to go about this, but the idea is assume they equal for the moment and see if that holds true.

We want to show this is true
Code: 
          1         2sqrt(3) - 1 
    ------------ = ------------
    2sqrt(3) + 1        11
A good place to start would be to clear the denominators. How do we do that?
 
Ah gee...posted this following your OTHER post:
.............................................................................................
bethany3168 wrote:
1 over 2 sqrt 3+1 = 2 sqrt 3-1 over 11 true or false?


Hmmm bethany...PLEASE use brackets; you'll go to your room with no
dessert if you keep this up :evil:

That should be shown like this:
1 / (2sqrt(3) + 1) = (2sqrt(3) - 1) / 11

We can cross-multiply next (like if a/b = c/d, then ad = bc):

(2sqrt(3) + 1)(2sqrt(3) - 1) = 11 * 1

(2sqrt(3))^2 - 1 = 11 : just like (x + y)(x - y) = x^2 - y^2

4*3 - 1 = 11 : 2^2=4 and sqrt(3)^2 = 3
12 - 1 = 11
Can you finish :wink:
 
Yes, Sir!

Okay, I follow you so far.

cross multiply 1 / (2sqrt(3) + 1) = (2sqrt(3) - 1) / 11

11*1=11

(2sqrt(3) + 1) = (2sqrt(3) - 1) / 11
4 sqrt (9)-1
4 sqrt (3)-1
12-1=11

11 and 11 are equal so yes, the equation is true? I would like something with strawberries...
 
Thank you Denis.

That looks AWESOME! Candles and everything. Yummm :) I am so lucky how many have teachers that reward them with praise AND dessert? :D
 
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