I have question can HP Prime Solve these two functions?

[tom234]

(05-11-2020 05:14 PM)Albert Chan Wrote:  

(05-11-2020 03:35 PM)swagner53 Wrote:  I entered the 2 equations as in the attached screen shot and got the 1,1 answer from the TI Inspire
as well as 2 other solutions (which makes sense for third order equations).

Actually, this is a 9-degree equation, with 3 real and 6 complex solutions

eqn2: y^3 + x*y^2 = 2     → x = (2-y^3)/y^2

eqn1: x^3 + 9*x^2*y = 10, substitute x from above

(8*y^9 - 30*y^6 + 24*y^3 + 8) / y^6 = 10
8*(y^9 - 5*y^6 + 3*y^3 + 1) = 0
8* (y^3 - 1) * ((y^3 - 2)^2 - 5) = 0

y^3 = 1, 2 ± √5
y = 1, φ ,1-φ, w, wφ ,w(1-φ), w², w²φ, w²(1-φ),       where w=exp(i*pi/3), φ=(1+√5)/2

got this is something wrong with this calculator
?