سوال ۲۰ کنکور ارشد ریاضی ۱۴۰۵

PASSAGE 2 (excerpt): Omar Khayyam ... is better known in the Eastern world as a mathematician, astronomer, and physicist. The solution of cubic equations by the Khayyam method of intersecting conic sections ... Khayyam's work made an important contribution to the development of algebra. Although he used geometric methods for the solution of cubic equations, he was keenly aware of the limitations of this method. Regretting the lack of a purely algebraic method of solving cubic equations, he admitted, "Neither we, nor any of those who are concerned with algebra have been able to prove this equation—perhaps others who follow us will be able to fill the gap." Others did follow, but not until 470 years later, when Cardano published a purely algebraic solution of cubic equations. Even so, Khayyam made a contribution by systematizing the study of cubic equations and finding geometric solutions for some that had previously remained unsolved. In Khayyam's time, mathematicians made many attempts to solve the cubic equations that arose from the study of optics and from the use of conic sections to solve the classical problems of duplicating the cube and trisecting any angle.

The passage provides sufficient information to answer which of the following questions? I. What were some of the age-old problems facing mathematicians in Khayyam's time? II. In what year was the Italian mathematician Gerolamo Cardano born? III. Who were some of the most prominent mathematicians living in Khayyam's era?