SOLUTION: Solve: cos^4a+cos^2a=1

Question 766558: Solve: cos^4a+cos^2a=1
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Solve: cos^4a+cos^2a=1
sub x for cos^2
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=5 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.618033988749895, -1.61803398874989. Here's your graph:

---------
cos^2 = 0.618034
cos =~ 0.78615
a =~ 38.1727 degs (principal value)
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