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a+b =? if a^3-a^2+a-5=0 and b^3-2b^2+2b+4=0

Source: 2016 Moldova JBMO TST p5

February 20, 2021
system of equationsSystemalgebra

Problem Statement

Real numbers aa and bb satisfy the system of equations {a3−a2+a−5=0b3−2b2+2b+4=0\begin{cases} a^3-a^2+a-5=0 \\ b^3-2b^2+2b+4=0 \end{cases} Find the numerical value of the sum a+ba+ b.
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