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a+b =? if a^3 - 3a^2 + 5a - 17 = 0 and b^3 - 3b^2 + 5b + 11 = 0

Source: 2002 Swedish Mathematical Competition p5

March 21, 2021
system of equationsSystemalgebra

Problem Statement

The reals a,ba, b satisfy {a3−3a2+5a−17=0b3−3b2+5b+11=0.\begin{cases} a^3 - 3a^2 + 5a - 17 = 0 \\ b^3 - 3b^2 + 5b + 11 = 0 .\end{cases} Find a+ba+b.
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