How do u find the formula of r when the formula is b=square root of 4a^2 r^2over 4r^2-a^2?Asap!?its so hard!!?

Question

thanks!!

Answer 1

(1) Is the entire fraction, numerator and denominator, BOTH under the square root? Or just the numerator "4a^2...r^2"
(2) Are you sure there is a minus sign -
between 4r^2 and a^2 in the denominator
but no sign + or - in the numerator?

If the entire fraction is under the sqrt, and if there is no -

b =
sqrt
[ 4a^2 * r^2
--------------
4r^2 * a^2]

= sqrt [1] = 1
============================
If there is a minus sign, square both sides to get

b^2 =
4a^2 * r^2
------------
4r^2 - a^2

multiply both sides by denominator to get
(b^2)(4r^2 - a^2) = 4a^2 * r^2

distribute b^2 across parentheses
(4r^2 * b^2) - (a^2 * b^2) = 4a^2 * r^2

(4r^2*b^2) - 4a^2 * r^2 = a^2 * b^2

4r^2(b^2 - a^2) = a^2 * b^2

r^2 =
a^2 * b^2
-------------
4(b^2 - a^2)

r = + or -
sqrt
[ a^2 * b^2
--------------
4(b^2 - a^2)]

= + or -
a*b
-------------
2 * sqrt [b^2 - a^2]


To get sqrt out of the denominator, multiply top and bottom
by that sqrt expression

= + or -
a * b * sqrt [b^2 - a^2]
----------------------------
2 (b^2 - a^2)
===================================
Test your answer:
Pretend a = 1, r = 2 and plug into original expression
which makes b = sqrt [16/15]
Plug these three values into final expression
r = 2 =
1 * sqrt[16/15] * sqrt[16/15 - 1]
-----------------------------------------
2 [16/15 - 1]

= 1 * sqrt [16/15] * sqrt [1/15]
---------------------
2 [ 1/15 ]

= 1 * sqrt(16)/15
--------------------
2/15

= 1 * 4
---------
2
which does = 2 = r

So this works if you mean everything on the right hand side, the whole fraction, is under the square root in the question.