Solution for Polynomial Degree 7: x2=k2-k2x7/2

[chhitiz]

can anyone tell me the solution of- x²=k²-k²x^7/2

 

[HallsofIvy]

(Is that first "-" a minus or a hyphen?)

If you let y= x^1/2, x²= k²- k²x^7/2 becomes y⁴= k²- k²y⁷ or k²y⁷+ y⁴- k²= 0. I see no simple way to factor that and, in general, solutions to polynomial equations of degree higher than 4 cannot be written in terms of algebraic functions.

 

[chhitiz]

i got that far as well. isn't there a formula for sum of product of roots n at a time, n-1 at a time and so on?