Assalamu alaikum, my name is Amirul Eduard and this video is about Omar Khayyam and his general cubic solution. His full name is Zia-Tal-Din Abdul-Mingh. He is the pro-hebron and the sub-brile Khayyami from the 10th of the AD in Nishankur, Shahirat. He is mostly known as a poet but had largely contributed in mathematics, philosophy and astronomy.
Today's video is about his general cubic solution which was found through geometry. You must be wondering, how do you do this? Well, one day, he was given a challenge.
The question goes as follows. Then, through many experimentations, Omar Khayyam was able to discover that only two objects were needed to solve cubic equations. In other words, by using two specific shapes on a graph, two solutions could be easily found.
Let's take a deeper look at how this method works. First, we're given the cubic equation. equation in the graph here, there is a parabola and a circle of r radius each within the equation. Note the two intersection points at origin and x1, y1 which is supposed to be the solution to the cubic equation. Let's check if point x1, y1 is a solution by putting them in the equations.
The parabola and circle equation can now be rewritten as these. We can now put them together and square both sides to get this equation. Finally, we can simplify to get this equation which is similar to the original cubic equation.
Thus we can conclude that point X111 is a solution. Let's try this with a real problem. Given a business that has a profit function that is equal to QQ means 400 Q and they would like to know what level of production would produce a profit level of 100,000 ringgit.
Thus the cubic equation would be this and if we draw the same graph as before by including these numbers we will get the point 43.547 and 94.8.8 Let's put 43.547 back into the original equation, and it's very close to 100,000 units in profits. This would mean that if the business produces at 44 units, it will achieve the profits it wanted, and that Omar Khayyam's method works. Fun fact, in Omar Khayyam's time, he was known to be the very first person that has integrated geometry and algebra together.
His research and findings bore inspirations to new scholars. which shows how influential these experiments were and how much he has contributed in the field of mathematics. That's all from me, thanks for watching!