By Bob Miller

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Structure and Representation of Jordan Algebras

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Extra info for Bob Miller's Algebra for the Clueless, 2nd edition (Miller, Robert, Clueless Series.)

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5, −3, −1, 1, 3, 5, 7, . . The difference between consecutive odds is also 2. We do the even and odd integer problems exxxxactly the same way. x = odd integer (the smallest); x + 2 = next consecutive odd integer (the middle); x + 4 = largest. x2 = square of the smallest; one more than the largest = x + 4 + 1; product (answer in multiplication) of the smallest and the middle = x(x + 2). x2 + x + 4 + 1 = x(x + 2) x2 + x + 5 = x2 + 2x x2’s cancel x + 5 = 2x x=5 The answers are 5, 7, and 9. As I said, most students like this kind of problem.