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AQA C4 June 2010, question 4b. How to answer?

question 4ai: Find the binomial expansion of (1+x)^3/2, which I got 1+3/2x + 3/8 x^2
question 4aii: Find the binomial expansion of (16+9x)^3/2, which I got 64+54x+243/32x^2

question 4b: Use your answer to part aii to show that 13^3/2 is approximately equal to 46 + a/b, stating the values of the integers a and b.

I've checked the mark scheme but it is really bad at showing how to do question 4b, so could someone please explain? Thanks.
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RMNDK
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Original post by dualghost
question 4ai: Find the binomial expansion of (1+x)^3/2, which I got 1+3/2x + 3/8 x^2
question 4aii: Find the binomial expansion of (16+9x)^3/2, which I got 64+54x+243/32x^2

question 4b: Use your answer to part aii to show that 13^3/2 is approximately equal to 46 + a/b, stating the values of the integers a and b.

I've checked the mark scheme but it is really bad at showing how to do question 4b, so could someone please explain? Thanks.


It's asking you to use this thing (16 + 9x)3/2 to estimate the value of 133/2
You have to make the bit in the brackets

i.e. 16 + 9x = 13.

Figure out that value of x.

Then substitute that value into your expansion that you figured out.
You'll see that it gives 46 + [a fraction].

This fraction is the a/b they're on about.
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Avatar for dualghost
dualghost
OP
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Thanks a lot :smile:

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