Solved: In 1224, Leonardo of Pisa, better known as Fibonacci, answered a mathematical

Chapter 2, Problem 10

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In 1224, Leonardo of Pisa, better known as Fibonacci, answered a mathematical challenge ofJohn of Palermo in the presence of Emperor Frederick II: find a root ofthe equation x 3 + 2a'2 + IOx = 20. He first showed that the equation had no rational roots and no Euclidean irrational rootthat is, no root in any of the forms a Vb, Va Vb, \/a \/b, or ~Ja \/A, where a and b are rational numbers. He then approximated the only real root, probably using an algebraic technique of Omar Khayyam involving the intersection of a circle and a parabola. His answer was given in the base-60 number system as

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