SOLUTION: I need to express the following problem in terms of B: a = 1/sq root of(1-B^2) I cannot figure out how to get rid of the square root since 1-b^2 simplifies to (1+B)(1-B)

Algebra ->  Equations -> SOLUTION: I need to express the following problem in terms of B: a = 1/sq root of(1-B^2) I cannot figure out how to get rid of the square root since 1-b^2 simplifies to (1+B)(1-B)      Log On


   

Question 242931: I need to express the following problem in terms of B:
a = 1/sq root of(1-B^2)
I cannot figure out how to get rid of the square root since 1-b^2 simplifies to (1+B)(1-B)
Found 2 solutions by jim_thompson5910, JimboP1977:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a=1%2Fsqrt%281-b%5E2%29 Start with the given equation.


a%2Asqrt%281-b%5E2%29=1 Multiply both sides by sqrt%281-b%5E2%29.


sqrt%281-b%5E2%29=1%2Fa Divide both sides by 'a'.


1-b%5E2=%281%2Fa%29%5E2 Square both sides.


1-b%5E2=1%2Fa%5E2 Square 1%2Fa to get 1%2Fa%5E2


-b%5E2=1%2Fa%5E2-1 Subtract 1 from both sides.


-b%5E2=1%2Fa%5E2-%28a%5E2%29%2F%28a%5E2%29 Multiply 1 by %28a%5E2%29%2F%28a%5E2%29


-b%5E2=%281-a%5E2%29%2Fa%5E2 Combine the fractions.


b%5E2=-%281-a%5E2%29%2Fa%5E2 Divide both sides by -1.


b%5E2=%28a%5E2-1%29%2Fa%5E2 Distribute


b=%22%22%2B-sqrt%28%28a%5E2-1%29%2Fa%5E2%29 Take the square root of both sides.


b=sqrt%28%28a%5E2-1%29%2Fa%5E2%29 or b=-sqrt%28%28a%5E2-1%29%2Fa%5E2%29 Break up the plus/minus


b=sqrt%28a%5E2-1%29%2Fsqrt%28a%5E2%29 or b=-sqrt%28a%5E2-1%29%2Fsqrt%28a%5E2%29 Break up the square root.


b=sqrt%28a%5E2-1%29%2Fa or b=-sqrt%28a%5E2-1%29%2Fa Simplify the square roots in the denominator.


So the solutions are: b=sqrt%28a%5E2-1%29%2Fa or b=-sqrt%28a%5E2-1%29%2Fa

Answer by JimboP1977(311) About Me  (Show Source):
You can put this solution on YOUR website!
a+=+1%2Fsqrt%281-B%5E2%29
I personally would rewrite in terms of powers:
a+=+%281-B%5E2%29%5E%28-1%2F2%29 1/2 means the square root (1-B^2) and the negative sign means to take the reciprocal of this result ie one divided by the result.
a%5E-2+=+1-B%5E2 raise both sides to the exponent -2. Remember that when you raise a power to a power you multiply them together so -1/2 * -2 = 1
1-a%5E%28-2%29+=+B%5E2 take one from both sides and multiply by -1
%281-a%5E%28-2%29%29%5E%281%2F2%29+=+B raise both sides to the power of 1/2