excellent❗️

Incidentally one of the solution is the golden number.

Alternatively you could note that for every tupel (x,y) that solves x + y^2 = y^3, the tupel (y, x) solves y + x^2 = x^3. Consider the location of the tupels relatively to the first main diagonal (y = x) and note: - If (x, y) is located above the main diagonal, (y, x) is below the main diagonal. - If (x, y) is located below the main diagonal, (y, x) is above the main diagonal. - If (x, y) is located on the main diagonal, (y, x) is also on the main diagonal. ==> All intersection points of both functions are located on the first main diagonal (y = x). ==> x + x^2 = x^3 0 = x (x - 0.5 - sqrt(5)/2) (x - 0.5 + sqrt(5)/2) x = 0 or x = 0.5 + sqrt(5)/2 or x = 0.5 - sqrt(5)/2

Muito bom! 👍