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I don't know how to solve the following equation: $x^5-h_1x^4-h_2x^3-h_5=0$, where $h_1=\beta_1+\beta_2$, $ h_2=\beta_1+\beta_2-\beta_1\beta_2-\frac{\beta_1\beta_2}{\beta_1+\beta_2}$, $h_5=\frac{(\beta_1\beta_2)^3}{(\beta_1+\beta_2)^2}$, where $1<\beta_1<\beta_2<\sqrt2$ , although I do know it is connected to the Galois theory....

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    I've removed [tag:algebra] tag, since we don't use algebra tag anymore, see [meta](http://meta.math.stackexchange.com/questions/473/the-use-of-the-algebra-tag/3081#3081) for details. Perhaps you could use [tag:abstract-algebra] or [tag:galois-theory], if you find these tags suitable for your question.2012-11-20

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