Question

#45 How many solutions exist for the equation (cos^2x/x)-(1/5)=0

Answer 1

45. A graphing calculator shows there to be 3 solutions. (There is no algebraic way to find them.)

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Rewriting the equation to

... f(x) = cos(x)² -x/5

We note sign changes in this function between 0 and π/2, between π/2 and π, and between π and 3π/2. Outside the range 0 to 3π/2, there are no more sign changes, hence no more solutions.

Answer 2

check the picture below.

notice, you're asked to use a graphing calculator to get them.