Math 331-3: MENU: Abstract Algebra Spring 2009

Week I: Let z = x + 1/x. Show that z^3 - 3*z = x^3 + 1/x^3. Use this to solve the equation z^3 - 3*z = L for any complex number L.

Show that any equation y^3 + a y^2 + b y + c = 0 can be transformed into the form z^3 - 3 z - L = 0 by a substitution of the form y = Az+B, where A and B can be obtained by (at worse) solving a quadratic equation with coefficients involving a,b, and c.

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