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Question: exercise 1013 use cardanos formula as clarified in exercise 1012...

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Exercise 10.13. Use Cardanos formula, as clarified in Exercise 10.12, to obtain all three solutions to the cubic equation y3-7y + 6 = 0. 1. Write down the solution given by the formula as a sum of cube roots. Observe that it involves the cube roots of 10 and 10 2. Using the numbers w and w2 and the earlier determination of one cube root of -3 +V-3, write expressions for the three complex numbers that are cube roots of -3+10V-3. Also write down the three complex numbers that are cube roots of -3 - 10V-3 3. Pair the cube roots of-3+0V/-3and -3-10V-3 as specified in Exercise 10.12 to get three pairs such that the product of the complex numbers in each pair equals 4. Add together the complex numbers in each pair to obtain all three solu tions of y3-7y + 6 = 0. Note that all three solutions are real.

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