Hi, this is the first time I have come across a question where x has appeared in an equation more than once so I am a bit stumped as how to find it.
55.17 = [(2x)^2]/[(2-x)(2-x)]
x = ?
I can simply it to:
55.17 = (4x^2) / [(2-x)^2]
55.17^(1/2) = 4x / (2-x)
but still can't find x
any help would be great
Thanks HallsofIvy,
solution 1.
K^1/2 = 2x / 2 - x
K^1/2 (2 - x) = 2x
[K^1/2 (2 - x )]/2 = x
(2.K^1/2 - x.K^1/2)/2 = x
(2.K^1/2)/2 = x + x.K^1/2
(2.K^1/2)/2.K^1/2 = 2x
(2.K^1/2)/4.K^1/2 = x
1/2 = x
solution 2.
K^1/2 = 2x / x - 2
K^1/2 (x - 2) = 2x
x.K^1/2 - 2K^1/2 = 2x
-2K^1/2 = 2x - x.K^1/2
(-2K^1/2) / K^1/2 = 2x - x
-K^1/2 = x
The answer can not be negative therefore solution 1 must be correct (as long as my working out is right).
EDIT: actually i think i must have done something wrong because the answer should utilize K, but i cancelled it out. Because the answer needs to be different for different values of K.
Can you guys point out my error?
Thanks again abhishekkgp,
solution 1.
K^1/2 = 2x / 2 - x
K^1/2 (2 - x) = 2x
[K^1/2 (2 - x )]/2 = x
(2.K^1/2 - x.K^1/2)/2 = x
(2.K^1/2)/2 = x + (x.K^1/2)/2
(4.K^1/2)/2 = 2x + x.K^1/2 <- but I still get stuck and can't separate the x's and the K's...
I tried it again and went this way:
K^1/2 = 2x / 2 - x
K^1/2 (2 - x) = 2x
K^1/2 (2 - x ) = 2x
2.K^1/2 - x.K^1/2 = 2x
2 - x = 2x / K^1/2
2 = (2x + x) / K^1/2
2.K^1/2 = 3x
(2.K^1/2) / 3 = x
Could that be right?
Also, if it is right, how come I am stuck in the first part in this post, is there a trick I am missing?