SOLUTION: I need help to find the product of each pair of conjugates. (2sqrt3 - sqrt7)(2sqrt3 + sqrt7)

Algebra ->  Square-cubic-other-roots -> SOLUTION: I need help to find the product of each pair of conjugates. (2sqrt3 - sqrt7)(2sqrt3 + sqrt7)      Log On


   

Question 309970: I need help to find the product of each pair of conjugates.
(2sqrt3 - sqrt7)(2sqrt3 + sqrt7)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If we let x=2%2Asqrt%283%29 and y=sqrt%287%29 we get the expression %28x-y%29%28x%2By%29. FOILing this expression gives us %28x-y%29%28x%2By%29=x%5E2-y%5E2 which is a difference of squares. Plug x=2%2Asqrt%283%29 and y=sqrt%287%29 back in to get




Now just multiply out and simplify the right side to get:


%282%2Asqrt%283%29-sqrt%287%29%29%282%2Asqrt%283%29%2Bsqrt%287%29%29=4%2A3-7


and do a bit more arithmetic to get


%282%2Asqrt%283%29-sqrt%287%29%29%282%2Asqrt%283%29%2Bsqrt%287%29%29=5