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Originally Posted by dhiab Calculate : are the roots of the equation . But . Therefore are the roots of the equation . Writing y = 1/x, you see that are the roots of the equation .
If we call the roots of that equation then we know that , and . Now successively compute that , , , , .
That looks like a large number, but if you compute the 8th powers of , and , you'll find that the sum comes out right.
Last edited by Opalg; Sep 13th 2009 at 01:36 PM.
Reason: Corrected arithmetic mistakes
My calculator gives this value: sec^8 (pi/9) + sec^8 (5pi/9) + sec^8 (7pi/9) > 1.2096
How to get a closed form answer for this? dhiab, any hint?
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