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 Solution by Praneeth)

Though xdog asked that his "oversight" post was to be disregarded, I, too, believe 8/b=-1 => b=-8.

Letting b=-8, and using a cubic equation calculator I get the roots
y₁ ~= 3.2360679775
Y₂ ~= -1.2360679775
y₃    = -2

Plugging these roots into the second given equation
y₁²/y₂ + y₂2/y₃ + y₃2/y₁= -8
confirms these roots as correct.

Edited on February 3, 2008, 9:19 pm

Posted by Dej Mar on 2008-02-03 01:49:41