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a^3- 3ab^2 = 8, b^3 - 3a^2b = 11, a^2+b^2 =?

Source: Norwegian Mathematical Olympiad 2002 - Abel Competition p2c

February 21, 2020

algebrasystem of equations

Problem Statement

a

and

b

are real numbers such that

\begin{cases} a^3-3ab^2 = 8 \\ b^3-3a^2b = 11 \end{cases}

then what is

a^2+b^2