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Homework Statement
Let ## \lambda ## be the real solutions to the equation ## \sqrt{\lambda +9}+\sqrt{2\lambda +17}=12 ##. Then what is the sum of the solutions ## z ##, with ## Re\ z>0 ##, of the equation ## z^4=\lambda -32 ##?
Homework Equations
The Attempt at a Solution
I tried substituting ## \lambda =z^4+32 ## into ## \sqrt{\lambda +9}+\sqrt{2\lambda +17}=12 ## to see if something simplified, but nothing did. Am I left with hacking this one out? Because I refuse to believe that I should try to actually solve ## \sqrt{\lambda +9}+\sqrt{2\lambda +17}=12 ## for ## \lambda ##.
Is there a "better" way?