The cubic equation y³ + by + b = 0 has three roots y₁, y₂ and y₃ with y₁ ≥ y₂ ≥ y₃, where b is real and non zero, such that:

y₁²/ y₂ + y₂²/ y₃ + y₃²/ y₁= -8

Determine y₁, y₂ and y₃

(In reply to exact solution by Daniel)

Well done, Daniel.

I have incorporated your methodology in the official solution.

Posted by K Sengupta on 2008-03-06 10:19:13