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Math Challenge III Algebra 2.29
Re: Math Challenge III Algebra 2.29
The equation in question is:
Solve for $z$: \[ \left(z+\frac{1}{z}\right)^2 + \left(z^2+\frac{1}{z^2}\right)^2 - \left(z+\frac{1}{z}\right)\cdot\left(z^2+\frac{1}{z^2}\right)\cdot\left(z^4+\frac{1}{z^4}\right)=3. \]It is good to expand the left hand side and clear the denominators, and then it is related to $z^{15}+1$.
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