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AQA C4 Binomial expansion approximation question help

Hey, I'm stuck on the approximation part of the binomial expansion chapter, the question which I'm trying to do is 7(b) here:

I got the answer for a(ii) correct as:

So using this I subbed in 0.04 for x and came out with this:

Which is wrong, I've been looking for some revision resources on approximation and I can't seem to find any good ones, would anyone be able to point out where my mistake is, thank you
Original post by Sayless

Which is wrong, I've been looking for some revision resources on approximation and I can't seem to find any good ones, would anyone be able to point out where my mistake is, thank you


What happens when you put x=0.04 into (a)(ii)? Not the expansion; the original function. It's not 1/root(3) as such, but rather a multiple of it.
If you substitute 0.04 into the first four terms of your expansion, you do indeed get 1.155.

However, if you substitute 0.04 into 1+5x1+2x \frac{1+5x}{\sqrt{1+2x}} , you get 233 \frac{2\sqrt{3}}{3} .

So you have 233=1.155 \frac{2 \sqrt{3}}{3} = 1.155 .

Now as a hint as to what to do next, think about how can manipulate 233 \frac{2\sqrt{3}}{3} to give 13 \frac{1}{\sqrt{3}}
Reply 3
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Sayless
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Original post by kingaaran
If you substitute 0.04 into the first four terms of your expansion, you do indeed get 1.155.

However, if you substitute 0.04 into 1+5x1+2x \frac{1+5x}{\sqrt{1+2x}} , you get 233 \frac{2\sqrt{3}}{3} .

So you have 233=1.155 \frac{2 \sqrt{3}}{3} = 1.155 .

Now as a hint as to what to do next, think about how can manipulate 233 \frac{2\sqrt{3}}{3} to give 13 \frac{1}{\sqrt{3}}


Ah right I get what you are saying, I have 233 \frac{2\sqrt{3}}{3}
if I times it by 1/2 I get 13 \frac{1}{\sqrt{3}} and if i divide it by 2 I also get 13 \frac{1}{\sqrt{3}} , but how do I show where I got the 2 or 1/2 from?
Original post by Sayless
Ah right I get what you are saying, I have 233 \frac{2\sqrt{3}}{3}
if I times it by 1/2 I get 13 \frac{1}{\sqrt{3}} and if i divide it by 2 I also get 13 \frac{1}{\sqrt{3}} , but how do I show where I got the 2 or 1/2 from?


From substituting x=0.04, you have:

23≈1.155\dfrac{2}{\sqrt{3}}\approx 1.155

Hence

13≈1.1552=...\dfrac{1}{\sqrt{3}}\approx \frac{1.155}{2}= ...

That's all there is to it.
Reply 5
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Sayless
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Original post by ghostwalker
From substituting x=0.04, you have:

23≈1.155\dfrac{2}{\sqrt{3}}\approx 1.155

Hence

13≈1.1552=...\dfrac{1}{\sqrt{3}}\approx \frac{1.155}{2}= ...

That's all there is to it.


Alright I get it now thanks a lot for your fast help!

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