solve

X to the power 15 + 1/ X to the power 25

when X + 1/X = 1

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- May 22nd 2008, 08:24 PMsktulikacompex numbers
solve

X to the power 15 + 1/ X to the power 25

when X + 1/X = 1 - May 22nd 2008, 09:31 PMmr fantastic
- May 22nd 2008, 10:03 PMmr fantastic
So you want to find the value of $\displaystyle x^{15} + \frac{1}{x^{25}}$ given that $\displaystyle x + \frac{1}{x} = 1$.

A brutal approach:

$\displaystyle x + \frac{1}{x} = 1 \Rightarrow x^2 - x + 1 = 0 \Rightarrow x = ......$. Express the solution in polar form.

$\displaystyle x^{15} + \frac{1}{x^{25}} = \frac{1}{x^{25}} (x^{40} + 1)$. Substitute the polar form of x, use de Moivre's theorem and tidy up.