C) Am I Solving this Hyperbolic Functions Homework Correctly?

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orbsoner
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Homework Statement


Attached is the problem


Homework Equations



My question is am i going about it the right way for question C). I have done A and B and am sure they are correct.


The Attempt at a Solution


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  • Printed homework problem on hyperbolic functions: solve 0 = 4x^3 + 3x - 2 using sinh, parts (a) to (c) with mark allocations of 5/15 each, showing the identity 0 = 4 sinh^3 y + 3 sinh y - sinh 3y and the solution x = sinh y = sinh((1/3) sinh^-1 2).
    question.PNG
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  • Handwritten working on lined paper for part c: substituting x = ct into 0 = ax^3 + bx + c, dividing by ac^3, and a line rearranging to 4t^3 + (4b/ac^2)t + (4b/ac^3)c = 0, then sinh 3y = -(4b/ac^3)c leading to c = 2 sqrt(b/3a).
    work.PNG
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orbsoner said:
[am i going about it the right way for question C).
I don't think so.
Look at how you solved b). What relationship between the coefficients did the method depend upon? E.g. suppose the constant term had been something other than -2. Would that have radically changed the method of solution? What about the other two?
When you've determined what the relationship is, you need to scale x to make the more general equation satisfy that relationship.