given that:
t=sin(18degrees)
what are the steps in solving:
(8t^4)-(8t^2)-t+1=0 ?
The original equation factors out to:
(t-1)(2t+1)(4t^2+2t-1)=0
Since we know t is sin(18), the first two factors will not equal zero, which leaves the final one.
Put that into the quadratic formula and one of the roots you get is (-1+sqrt(5))/4
(-1+sqrt(5))/4=sin(18)