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1

Clear["Global`*"] roots[Lv_?NumericQ, nv_?NumericQ, kv_?NumericQ, hv_?NumericQ] := Module[{L, n, k, h}, {L, n, k, h} = Rationalize[{Lv, nv, kv, hv}, 0]; Solve[{ 2*Cot[x] == k/(h (L/n)) x - h (L/n)/k/x, 60 > x > 0}, x, Reals]] The exact solutions are Root objects sol1 = roots[0.25, 20, 16, 0.1] These are approximately sol1 // N (* {{x -...


4

Your equation might be transformed to 2 Cot[x] == x/p - p/x with a new parameter p= (h (L/n) )/k With p0=(h (L/n) )/k /. {L -> 0.25, n -> 20, k -> 16, h -> 0.1}; (*0.000078125*) you might visualize the solution with ContourPlot ContourPlot[ContourPlot[1/(2 Cot[x]) == 1/((x/p) - p/x), {x, 0, 60}, {p, 0, 2 p0},FrameLabel -> {x,"p=\!\(\*...


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