Hi,
This is also very interesting to try and solve using a "hunt and peck" method, where you try different values and plug them into the network equation and solve numerically for a min in one circuit and a max in the other circuit. It becomes immediately apparent that the value of C is uniquely linked to the value of L, and that R sets the "channel spacing" between frequencies of the series and parallel. That gives you some organized method to optimize L and doesnt take forever to find by 'hand'.
Analytically, you can use the series resonant frequency to immediately eliminate one variable, either C or L, because of their unique relationship to each other and that constant series resonate point. You can then also solve for R as a function of L, and Fp as a function of L and R, then insert the equation for R into Fp and solve for L as a function of Fp, then insert the constant Fp and that provides for the best numerical value of L, then calculate R, then C.
If you would like to compare your final calculation to the best possible values (to about 14 digits of precision) then post your final values for L, C, and R here later.
In this kind of problem i would bet that the definition of the resonate frequency is the min current for one circuit and the max current for the other circuit.