SOLUTION: the problem is radical 3+2n + radical 2-2n =3, when i type radical it means the 3+2n and 2-2n are under the radical sign. i hope you can help me understand.

Algebra ->  Radicals -> SOLUTION: the problem is radical 3+2n + radical 2-2n =3, when i type radical it means the 3+2n and 2-2n are under the radical sign. i hope you can help me understand.      Log On


   

Question 182132This question is from textbook college algebra
: the problem is radical 3+2n + radical 2-2n =3, when i type radical it means the
3+2n and 2-2n are under the radical sign. i hope you can help me understand. This question is from textbook college algebra

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
the problem is radical 3+2n + radical 2-2n = 3,
:
sqrt%283%2B2n%29 + sqrt%282-2n%29 = 3
:
sqrt%283%2B2n%29 = 3 - sqrt%282-2n%29
square both sides:
3 + 2n = (3 - sqrt%282-2n%29)^2
FOIL the right side
3 + 2n = 9 - 6sqrt%282-2n%29 + (2-2n)
:
3 + 2n = 9 + 2 - 6sqrt%282-2n%29 - 2n
:
3 + 2n = 11 - 6sqrt%282-2n%29 - 2n
:
3 - 11 + 2n + 2n = -6sqrt%282-2n%29
:
4n - 8 = -6sqrt%282-2n%29
:
square both sides, FOIL the left side
16n^2 - 64n + 64 = 36(2-2n)
:
16n^2 - 64n + 64 = 72 - 72n
:
16n^2 - 64n + 72n + 64 - 72 = 0
:
16n^2 + 8n - 8 = 0
Simplify, divide by 8
2n^2 + n - 1 = 0
Factors to
(2n - 1)(n + 1) = 0
Two solutions:
n = 1%2F2
n = -1
:
:
Check both solution in original equation:
n = .5
sqrt%283%2B2%28.5%29%29 + sqrt%282-2%28.5%29%29 = 3
sqrt%283%2B1%29 + sqrt%282-1%29 = 3
sqrt%284%29 + sqrt%281%29 = 3; a good solution
:
n = -1
sqrt%283-2%29 + sqrt%282-%28-2%29%29 = 3
sqrt%281%29 + sqrt%284%29 = 3; also a good solution