a^3+b^3=20, using the formula of sum of cubes, we get (a + b)(a^2 - ab + b^2) = 20 => 5(a^2 - ab + b^2) = 20 => (a^2 - ab + b^2) = 4. Completing the square we have a^2 - ab + b^2 +2ab - 2ab = 4 => (a + b)^2 - 3ab = 4 => 5^2 - 3ab = 4 => 25 - 3ab = 4 => 3ab = 21 => ab = 7. Arrived at the simplest system ab = 7, a + b = 5
[input]solve(ab = 7, a + b = 5,a,b)[/input]
This equation has no roots (Discriminant of the intermediary quadratic equation is a negative number.)
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