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#1 2007-08-05 07:49:16

tony123
Member
Registered: 2007-08-03
Posts: 228

geometric mean -1/2

Prove that the three numbers cos40°, cos80° and cos160° have arithmetic mean 0, harmonic mean 1/2 and geometric mean -1/2.

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#2 2007-08-11 03:51:04

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: geometric mean -1/2

WHAT?! Nobody has answered this question yet? Shame on you all! shame

Use the triple-angle formula for cos:

Hence cos40°, cos80° and cos160° are all the distinct roots of the equation 8x[sup]3[/sup] − 6x + 1 = 0.

Now you can answer the question. roll

Last edited by JaneFairfax (2007-08-11 04:10:43)

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