\end{array}\right. 2. [Example] (from Mathematical Treatise in Nine Sections) Find a root of the equation x² – 71, 824 = 0, by carrying out the following steps: (a) Take 200 as an initial approximation and reduce the roots by 200 through the transformation y = x – 200. (b) With 60 as an approximation to the roots of the transformed equation, make a second substitution z = y – 60. (c) By trial, find an integral root z of the third equation and use it to obtain the desired root x. By letting y = x – 200 and z = y – 60, we get the equation z² + 520 z – 4224 = 0. Trial shows that z = 8 is a solution. O Use the above method to find a root of the equation x^2 – 65536 = 0.

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