Hi, my question is :

Let n be a positive integer. Find all real numbers x such that

I find that there is no such REAL number.

Does someone find a different answer?

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- Jan 13th 2009, 05:52 PMvincisonfireComplex Number
Hi, my question is :

Let n be a positive integer. Find all real numbers x such that

I find that there is no such REAL number.

Does someone find a different answer? - Jan 13th 2009, 06:03 PMProve It
- Jan 13th 2009, 06:09 PMMush
Well a pretty obvious solution from inspection is that if n is even, then x = 0 is a real number solution. But I'll do the working just to see if any others lurk:

Get all x terms on LHS and non-x terms on RHS

Hence for any positive integer.

For

Hence the equation has a real number solution for all even values of n. And that solution is . 0 is a real number. - Jan 13th 2009, 06:10 PMvincisonfire
Shouldn't it be because the angle will be

- Jan 13th 2009, 06:11 PMProve It
- Jan 13th 2009, 06:19 PMvincisonfire
I would thus have but it does not work.

And thanks Mush. I guess there is no solution for all n. - Jan 13th 2009, 06:37 PMNonCommAlg
the solutions are just put and solve a simple equation.

- Jan 13th 2009, 06:45 PMvincisonfire
Mush somewhere you did *

- Jan 13th 2009, 06:53 PMProve It
- Jan 13th 2009, 06:56 PMvincisonfire
To NonCommAlg :

I don't understand why but as n goes up the solutions are not working???

e.g. when n = 101 mathematica gives me 2.59828*10^167 + 0. I - Jan 13th 2009, 07:00 PMvincisonfire
Yes it should be . That complicates the things ... but the answer is still good.

- Jan 13th 2009, 07:05 PMNonCommAlg
- Jan 13th 2009, 07:09 PMvincisonfire
No I meant

When n > 10 it begins to have great values. - Jan 13th 2009, 07:14 PMProve It
OK this is driving me mad.

According to my CAS, it reduces to...

and gives

and . - Jan 13th 2009, 07:16 PMNonCommAlg