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Omar Khayyam's approach to solving certain cubic equations

Omar Khayyam (al-Khayyami, 1048-1131), mathematician, philosopher and poet laid down the gauntlet for the algebraic solution of cubic equations. Here we see how he tackled , where and are given positive constants. To solve the given cubic equation using Khayyam's method, let |AB| = and |BC| = . Construct the semi-circle on diameter BC and the parabola , as shown, intersecting at D. Complete the rectangle BEDZ. Then satisfies the given cubic.