Problem

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Tags: algebra proposed, algebra



Given real numbers $x$ and $y$. Let $s_{1}=x+y, s_{2}=x^2+y^2, s_{3}=x^3+y^3, s_{4}=x^4+y^4$ and $t=xy$. a) Prove, that number $t$ is rational, if $s_{2}, s_{3}$ and $s_{4}$ are rational numbers. b) Prove, that number $s_{1}$ is rational, if $s_{2}, s_{3}$ and $s_{4}$ are rational numbers. c) Can number $s_{1}$ be irrational, if $s_{2}$ and $s_{3}$ are rational numbers?