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How may I get the function of the intersection of the two areas as displayed in figures g1 and g2.

the code of g1 is

g1 = Plot3D[(0.5` ((0.25` + k \[Theta])/(1 + 0.25` k \[Theta]))^0.5`)/   k^0.5` + (0.5` k^0.5` (\[Theta]/(1 + 0.25` k \[Theta]) - (0.25` \[Theta] (0.25` + k \[Theta]))/(1 + 0.25` k \[Theta])^2))/((0.25` + k \[Theta])/(1 + 0.25` k \[Theta]))^0.5`, {k, 1, 2}, {\[Theta], 0.5, 10}, AxesLabel -> {"k", "\[Theta]", "Abl"}, PlotStyle -> {Blue}]

the code of g2 is

g2 = Plot3D[1, {k, 1, 2}, {\[Theta], 0.5, 10},   AxesLabel -> {"k", "\[Theta]", "Abl"}]

Then the code

Show[g1,g2]

enter image description here

gives a graphical representation within a 3D-plot I would be happy to learn. thx Ina

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You can use Solve for this:

sol = Solve[(0.5` ((0.25` + k \[Theta])/(1 + 0.25` k \[Theta]))^0.5`)/
    k^0.5` + (0.5` k^0.5` (\[Theta]/(1 + 
           0.25` k \[Theta]) - (0.25` \[Theta] (0.25` + 
             k \[Theta]))/(1 + 0.25` k \[Theta])^2))/((0.25` + 
         k \[Theta])/(1 + 0.25` k \[Theta]))^0.5` == 1, k]

To plot:

Plot[k /. 
  sol, {\[Theta], 0.5, 10}]

enter image description here

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