problem is as follows:
An attenuator is designed to conform to the condition that,
eqn 1: (R1 + R2 + Ro) /R2 = 5

where Ro = sqrt(R1R2 +( R1^2) /4) = 60

find value of R1 and R2 (note in practice no negative resistance)
I am working through some of my very old books and have got stuck on procedure to break this code. I have the answers but need a nudge on how to go about this one. Any help is much appreciated so i can stop having sleepless nights and mathematical nightmares.
Thanks for you help

 

Start off my getting all references to R2 to the right hand side of the eqn1.

 

problem is as follows:
An attenuator is designed to conform to the condition that,
eqn 1: (R1 + R2 + Ro) /R2 = 5

where Ro = sqrt(R1R2 +( R1^2) /4) = 60

find value of R1 and R2 (note in practice no negative resistance)
I am working through some of my very old books and have got stuck on procedure to break this code. I have the answers but need a nudge on how to go about this one. Any help is much appreciated so i can stop having sleepless nights and mathematical nightmares.
Thanks for you help

Since there's no circuit schematic, there's no way for us to know if your starting equations make sense.

For Ro, which of the following do you mean:

\(
R_o \; = \; \sqrt{R_1R_2 \; + \; \frac{\left( R_1^2\right)}{4}}
\)

which is what you wrote, or

\(
R_o \; = \; \sqrt{\frac{R_1R_2 \; + \; R_1^2}{4}}
\)

which is what someone might easily have meant.

If R1 is supposed to be ~71 Ω, then you meant the first, but if R1 is supposed to be ~101 Ω, then you need the latter.

In either case, solving it is pretty straight forward if you tackle it in two steps.

The first step is to use the first equation to solve for R2 in terms of R1.

Then substitute this into the second equation and solve the resulting quadratic equation.

 

Thanks for the replies. There is no circuit, its just a problem from my old text. Relates to some attenuator eqn.
WBahn, thanks for redoing the eqn. in better format. The first example you show is correct. having another look at what I posted I seem to have left out meaning full brackets. Looks like you have solved it as 71 ohms is correct for R1.
I will now need to readdress the issue and work out the correct method for solution.
thanks all.