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Old HSC Question Help (1 Viewer)

Jonomyster

New Member
Joined
Apr 8, 2018
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9
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Male
HSC
2018
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!!
 

aa180

Member
Joined
Sep 21, 2016
Messages
39
Location
Euclidean 3-space
Gender
Male
HSC
2012
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 .
 
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