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The video demonstrates how to find the roots of a number using the equation x^3 + y^2 = z^2. If x is equal to zero, the equation has no solutions. However, if x is not equal to zero, there are two solutions: x = 0 or x = ±1. The video then calculates the solutions for x = 0 and x = ±1, and shows how to find the third root of the equation using the quadratic equation.
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