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I have this system of equation: [tex] A = \frac{\alpha + \beta + \gamma}{3}[/tex] [tex] B = \sqrt[2]{\frac{\beta \gamma + \gamma \alpha + \alpha \beta}{3}}[/tex] [tex] C = \sqrt[3]{\alpha \beta \gamma}[/tex] And I want to solve this system for α, β and γ. In other words, I want to express α, β and γ in terms of A, B and C.
[tex] \alpha = \alpha (A,B,C)[/tex][tex] \beta = \beta (A,B,C)[/tex][tex] \gamma = \gamma (A,B,C)[/tex]
[tex] \alpha = \alpha (A,B,C)[/tex][tex] \beta = \beta (A,B,C)[/tex][tex] \gamma = \gamma (A,B,C)[/tex]