solve:
tan^2(x) + ( 1 - root(3))tan(x) = root(3) for x E [0, 2pi]
my method:
(tan(x))^2 = tan(x)(1-root(3)) = root(3)
let tan(x) = a
a^2 + a-a(root(3)) - root(3) = 0
a(a+1) - root(3)(a+1) = 0
a(a+1) = root(3)(a+1)
therefore a = root(3)
tan(x) = root(3)
sin(x)/cos(x) = root(3)
...
x = pi/3 and 4pi/3
what have i done wrong/not enough?
actually wait! duh i forgot, or a = -1
but is my solution legitimate?
kilbaha solution have done it another method
Did you get the same solution? I suppose Kilbaha probably used the quadratic method.
My answers were, x = pi/3, 3pi/4, 4pi/3, 7pi/4
I'll post a scan of my method here, just let me scan and upload...
I assume your solution is equally as valid. Did Kilbaha solve it the way I did?