(a) Show that a root x 0 of the equation x 4 px 3 + q...

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(a) Show that a root x0 of the equation x4 – px3 + q = 0 is a repeated root if and only if 4x0 – 3p = 0

(b) The stiffness of a rectangular beam varies with the cube of its height h and directly with its breadth b. Find the section of the beam that can be cut from a circular log of diameter D that has the maximum stiffness.

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