given that:
t=sin(18degrees)
what are the steps in solving:
(8t^4)-(8t^2)-t+1=0 ?
Hello, jonathanraxa!
I don't understand . . .
Given that: .$\displaystyle t \:=\:\sin(18^o)$
what are the steps in solving: .$\displaystyle 8t^4 - 8t^2 -t+1\:=0\:\,?$
We don't have to solve the equation!
They gave us the answer! .$\displaystyle t \:=\:\sin18^o$
Can you give us the original wording of the problem?
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)