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File:Omar Khayyám's solution of third degree equations.png

Omar_Khayyám's_solution_of_third_degree_equations.png (392 × 404 pixels, file size: 7 KB, MIME type: image/png)

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Português: Método de Omar Khayyám de resolução de equações de terceiro grau. Para resolver a equação x^3 + 200x = 20x^2 + 2000, considera-se a equação x^4 - 30x^3 + 400x^2 - 4000x + 20000 = 0, que tem as mesmas soluções, para além da solução x = 10. As soluções desta equação são as abcissas da intersecção da circunferência x^2 - 30x +y^2 - sqrt(800)y + 400 = 0 e da hipérbole xy = sqrt(20000).
English: Omar Khayyám's method of solving third degree equations. In order to solve the equation x^3 + 200x = 20x^2 + 2000, one considers the equation x^4 - 30x^3 + 400x^2 - 4000x + 20000 = 0, which has the same solutions, besides 10. The solutions of this equation are the x-coordinates of the intersection points of the circle x^2 - 30x +y^2 - sqrt(800)y + 400 = 0 and the hyperbola xy = sqrt(20000).
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