moneybird
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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agdgdgdgwngo
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0?
moneybird
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i don't know the solution
agdgdgdgwngo
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\( 2 \pi \) ?
moneybird
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how do you get that?
Mertsj
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What course are you taking moneybird that this problem came from?
moneybird
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Grade 10 math
Mertsj
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ty
Mertsj
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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
moneybird
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how about 1 factor is 4, and 1 factor is 1/4
Mertsj
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That could not be true. The largest value of the cos is 1
Mertsj
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So the largest value of 2cos x is 2
jadest
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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
Mertsj
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Regardless of the value of x
moneybird
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Let me think about it
sunsetlove
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good work