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Thread: Old HSC Question Help

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    Old HSC Question Help

    So I was doing this question from the 1967 4U HSC which is as follows:










    Anyway, here is my progress on the problem:





















    So since I have solved the problem, you might be wondering why I am even making this post. The reason why is that the 1967 HSC has no solutions that I could find, and I am pretty sure that such a solution would make use of the partial fractions in the very first line of this post, which I did not. I am also quite interested in what a solution using partial fractions would look like as it could have some interesting techniques, tricks, etc. If anyone has any insights into solving the problem with partial fractions that would be greatly appreciated. Thanks!!

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    Re: Old HSC Question Help

    Quote Originally Posted by Jonomyster View Post
    So I was doing this question from the 1967 4U HSC which is as follows:










    Anyway, here is my progress on the problem:





















    So since I have solved the problem, you might be wondering why I am even making this post. The reason why is that the 1967 HSC has no solutions that I could find, and I am pretty sure that such a solution would make use of the partial fractions in the very first line of this post, which I did not. I am also quite interested in what a solution using partial fractions would look like as it could have some interesting techniques, tricks, etc. If anyone has any insights into solving the problem with partial fractions that would be greatly appreciated. Thanks!!
    Basically, you have:



    Use the trick



    Do the same for and combine like terms with the appropriate terms from the expansion to facilitate direct comparison of coefficients with the LHS, as well as bring the trailing terms on both expansions together over a common denominator to get your expression for .
    Last edited by aa180; 3 Oct 2018 at 12:25 AM.
    Jonomyster likes this.

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