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 2 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: \[(2 \cos (8x)  1)(2 \cos (4x)  1)(2 \cos (2x)  1)(2 \cos (x)  1) = 1\]?
 2 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: \[(2 \cos (8x)  1)(2 \cos (4x)  1)(2 \cos (2x)  1)(2 \cos (x)  1) = 1\]?

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moneybird
 2 years ago
Best ResponseYou've already chosen the best response.3i don't know the solution

Mertsj
 2 years ago
Best ResponseYou've already chosen the best response.0What course are you taking moneybird that this problem came from?

Mertsj
 2 years ago
Best ResponseYou've already chosen the best response.0This 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

moneybird
 2 years ago
Best ResponseYou've already chosen the best response.3how about 1 factor is 4, and 1 factor is 1/4

Mertsj
 2 years ago
Best ResponseYou've already chosen the best response.0That could not be true. The largest value of the cos is 1

Mertsj
 2 years ago
Best ResponseYou've already chosen the best response.0So the largest value of 2cos x is 2

jadest
 2 years ago
Best ResponseYou've already chosen the best response.2The maximum of every parenthetical is 1, the minimum is 2. You would need multiplicative inverses and even factors of positive for this to work

Mertsj
 2 years ago
Best ResponseYou've already chosen the best response.0Regardless of the value of x

moneybird
 2 years ago
Best ResponseYou've already chosen the best response.3Let me think about it
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