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Topic review (newest first)
- Milos
- 2005-05-14 23:09:48
n e time
- MathsIsFun
- 2005-05-13 20:50:01
Thanks, Milos ... 
TEAMWORK !
- Milos
- 2005-05-13 20:20:21
2AB = 2x - 1 ^2
4A^2B^2=4x^2 - 2x + 1
Now: A=sqr(x+1); B=sqr(x-1)
4x^2-4=4x^2 - 4x + 1
then:
4x=5
x=5/4
It was easy, because administrator has finished the difficult part.
- MathsIsFun
- 2005-05-13 10:45:49
Cool ... I will leave it for someone else then ...
Good luck.
- im really bored
- 2005-05-13 10:44:13
I know, but i can handle that. It was just my approach that was getting me. I was trying to go at it in a more complicated way
- MathsIsFun
- 2005-05-13 10:41:38
Well, we still aren't ALL the way there ... we still have 2AB to solve
- im really bored
- 2005-05-13 10:33:45
Wow it makes alot more sense putting it that way, I was tying to aproach it from some other way, which turned out horrible.Thanks for the help I understand it now
- MathsIsFun
- 2005-05-13 10:30:52
For simplicity, let's call sqrt(x+1) "A" and sqrt(x-1) "B"
You have: (A+B)/(A-B) = (4x-1)/2
Multiply both sides by (A+B)*(A-B): (A+B)*(A-B) * (A+B)/(A-B) = (A+B)*(A-B) * (4x-1)/2
Cancel: (A+B)^2 = (A+B)*(A-B) * (4x-1)/2
Expand: A^2 + 2AB + B^2 = (A^2 - B^2) * (4x-1)/2
Substitute A^2 = (x+1) and B^2 = (x-1): (x+1) + 2AB + (x-1) = ((x+1) - (x-1)) * (4x-1)/2
Simplify: 2x + 2AB = 2 * (4x-1)/2
More: 2x + 2AB = 4x - 1
More: 2AB = 2x - 1
- MathsIsFun
- 2005-05-13 09:54:16
I will work on it ...
I think the trick will be to multiply by [sqrt(x+1)-sqrt(x-1)]^2
Anyway, let's try and see how far we get
[sqrt(x+1)-sqrt(x-1)] * [sqrt(x+1)+sqrt(x-1)] = [sqrt(x+1)-sqrt(x-1)]^2 * (4x-1)/2
sqrt(x+1) * sqrt(x+1) + sqrt(x+1) * sqrt(x-1) - sqrt(x-1) * sqrt(x-1) - sqrt(x-1) * sqrt(x-1) = ...
(x+1) + (terms cancel each other) - (x-1) = ...
2 = [sqrt(x+1)-sqrt(x-1)] * [sqrt(x+1)-sqrt(x-1)] * (4x-1)/2
2 = [sqrt(x+1) * sqrt(x+1) - sqrt(x+1) * sqrt(x-1) - sqrt(x-1) * sqrt(x+1) + sqrt(x-1) * sqrt(x-1)] * (4x-1)/2
2 = [(x+1) - 2 * sqrt(x+1) * sqrt(x-1) + (x-1)] * (4x-1)/2
2 = [2x - 2 * sqrt(x+1) * sqrt(x-1) ] * (4x-1) / 2
4 = [2x - 2 * sqrt(x+1) * sqrt(x-1) ] * (4x-1)
Hmmm ... that helped a bit, let's try it again but using [sqrt(x+1)+sqrt(x-1)] * [sqrt(x+1)-sqrt(x-1)]
- im really bored
- 2005-05-13 09:34:40
I'm having trouble doing this problem:
solve for x
(square root of ( x + 1) + (square root of (x - 1) 4x - 1
_________(divided by)_____________________ = ___(divided by)___
(square root of ( x + 1) - (square root of (x - 1) (2)