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x + y = 2 and x^3 + y^3 = 3, x^2+y^2 =?

Source: Norwegian Mathematical Olympiad 2003 - Abel Competition p1a

February 21, 2020
system of equationsalgebra

Problem Statement

Let xx and yy are real numbers such that {x+y=2x3+y3=3\begin{cases} x + y = 2 \\ x^3 + y^3 = 3\end{cases} What is x2+y2x^2+y^2?
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