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a^2 + b^2 + c^2 > 2, a^3 + b^3 + c^3 <2, a^4 + b^4 + c^4 > 2

Source: 1977 Swedish Mathematical Competition p6

March 26, 2021
inequalitiesSystemalgebra

Problem Statement

Show that there are positive reals aa, bb, cc such that {a2+b2+c2>2a3+b3+c3<2a4+b4+c4>2\left\{ \begin{array}{l} a^2 + b^2 + c^2 > 2 \\ a^3 + b^3 + c^3 <2 \\ a^4 + b^4 + c^4 > 2 \\ \end{array} \right.
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