A2 binomial estimation question

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#1
Can someone please explain how I would choose a value of x for the part c estimation below please?

My thinking was make (1+3x)/(1-x) = 1/5 rather than 5 so I could just do 1/estimation at the end, but this gives 2.13333, but the answer's 2.2361.
Thanks

Last edited by Rhys_M; 1 month ago
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1 month ago
#2
Instead of using 1/5, you want the number to be close to 1 (x small) and of the form
5k^2
or similarly
5/k^2
The first one isn't close to 1 for integer k, the second one can be. You used the second one with k=5 which means x is relatively large and hence poor accuracy, but you had the right idea.
Last edited by mqb2766; 1 month ago
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#3
(Original post by mqb2766)
Instead of using 1/5, you want the number to be close to 1 (x small) and of the form
5k^2
or similarly
5/k^2
The first one isn't close to 1 for integer k, the second one can be. You used the second one with k=5 which means x is relatively large and hence poor accuracy, but you had the right idea.
So for these kind of questions in general you should make the original expression equal to a value in the form
(the original number) / a square number
Which is as close to one as possible.
So for this example it would be like 5/4 ?
Last edited by Rhys_M; 1 month ago
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1 month ago
#4
You want x to be small for your quadratic approximation to be accurate, so this fraction will be close to 1. So looking for a 5/k^2 is a natural thing to try as you can root it easily to get sqrt(5)/k.

Tbh, you could reverse engineer it as you know sqrt(5) ~ 2.2, so you'd want to divide by 2 to get it close to one, so ...
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