Most of us will have no problem in solving simple linear equations like 0=3x+7,

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Most of us will have no problem in solving simple linear equations like 0=3x+7, x=? Or even a slightly tricker quadratic equations such as 0=4x2-2x-7, x=? This is bread-and-butter stuff for secondary school students. But you are bright and enthusiastic university maths students looking for a challenge. bring in on. indeed. so why not solve this cubic equation 0=4x3+3x-2, x=? should be a piece of cake? not so fast young grasshopper. as you will soon see the answer involves hyperbolic functions (surprised?). so let the games begin. show, using the standard definitions of sin h(y), that 0 = 4sinh3 y+3 sinh y-sinh 3y use the result of part to show that a solution to 0=4x3+3x-2 is x=sin h y = sin h(1/3sinh-1 2) generalize this result to cubics of the form 0=ax3+bx+c where a and b are positive real numbers.

Explanation / Answer

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