## anonymous 4 years ago What is the ordered pair of positive intgers (a,b) for which a/b is a reduced fraction and $x = \frac{a \pi}{b}$ is the least positive solution of the equation: $(2 \cos (8x) - 1)(2 \cos (4x) - 1)(2 \cos (2x) - 1)(2 \cos (x) - 1) = 1$?

1. anonymous

0?

2. anonymous

i don't know the solution

3. anonymous

$$2 \pi$$ ?

4. anonymous

how do you get that?

5. Mertsj

What course are you taking moneybird that this problem came from?

6. anonymous

7. Mertsj

ty

8. Mertsj

This equation will be true if each factor = 1. Each factor will equal 1 if x = 0. So a/b, which must be 2 positive integers is 2/1

9. anonymous

how about 1 factor is 4, and 1 factor is 1/4

10. Mertsj

That could not be true. The largest value of the cos is 1

11. Mertsj

So the largest value of 2cos x is 2

12. anonymous

The maximum of every parenthetical is 1, the minimum is -2. You would need multiplicative inverses and even factors of positive for this to work

13. Mertsj

Regardless of the value of x

14. anonymous