The problem involves finding solutions to the quintic equation 16x5 - 20x3 + 5x + 1 = 0, using the relationship cos5θ = 16cos5θ - 20cos3θ + 5cosθ. The original poster attempts to relate the variable x to cosθ and explore the implications of cos5θ being equal to -1.
Participants are actively engaging with the problem, exploring the relationship between the angles and the quintic equation. Some guidance has been offered regarding how to identify the relevant solutions, but there is no explicit consensus on the final answers yet.
There is an emphasis on the limited number of distinct values for cosθ, despite the infinite solutions for θ. The discussion hints at the constraints of the homework problem, including its relatively low mark value.
conorordan said:
tiny-tim said:hi conorordan!
that's right!
so what are the 3 solutions to cos5θ = -1 ?
conorordan said:
…tiny-tim said:agreed
but don't lose the plot
you're only interested in cosθ (=x), and there aren't infinitely many values of that!
tiny-tim said:no
write on one line the infinitely many solutions for θ
write on the next line the values of cosθ for those values of θ
on the next line, cross out any duplicates …
how many are left?
)tiny-tim said:(you mean 3π/5