I, too, was not able to read Prime 3.1 files and can now see what you are doing.
Did you notice that different alphas in your sheet look different.
Some are formatted as constant and refer to the predefined constant alpha = 0.007297...
Only the alpha in the exponent is labeled as "variable" (or better, its labeled "-", meaning autodetect).
If I retype your expression the same way you did, I get an answer from the symbolic processor. I don't see, why you didn't and you haven't included the error message (it may be meaningless, anyway) in the picture.
I guess, the result I got is not what you wanted, as of the different alphas.
If I change the constants alphas to variables, the symbolics can't find a solution. I would have been surprised if the symbolics could come up with a solution for that equation (EDIT: and now, that the symbolics actually found a solution, I am surprised 
).
My next try was a solve block and given a guess value greater that 1 it find a solution. Hope this is what you are looking for.
As you can see I had to turn lambda11 and lambda22 into functions dependent on alpha.
Attached sheet is in Prime 3.0 format and you should be able to read it without problems with P3.1-
EDIT: I just realized that the last result is the very same which I got in the first place using the symbolics. Now I am a bit confused 
You'll have to double check the answer.
EDIT2: That behavior of Prime is quite strange and inconsequential. While we see that alpha is interpreted as predefined constant in the first picture, when it comes to solving, the symbolics interprets alpha as the to solve for variable and we get the correct solution.
In the second picture, when we manually set the two alphas to label "variable" , the symbolics fails, for reasons unknown to me. But if we label all the other alphas (which are set to "-", meaning automatic labeling) manually at "variable", the symbolics again finds the solution. Strange!
