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# binomial expansion

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1. Hi Guys,
does anybody know how you have to calculate the value of x in a given binomial expansion to find an estimate value of an expression?i got stuck on the question below if anyone help me to find our how to find out the value of x would be such great help. thanks
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2. (Original post by Alen.m)
Hi Guys,
does anybody know how you have to calculate the value of x in a given binomial expansion to find an estimate value of an expression?i got stuck on the question below if anyone help me to find our how to find out the value of x would be such great help. thanks
You have to work it out from what you've expanded and how you can choose x so that it looks like what you're trying to calculate. (Notice that 1/81 looks like a square number).

In some expansions you can find the number directly, other times (eg you've expanded (8-0.1x)^(1/2) and you want to find the square root of 710, you find 10 * sqrt 7.1 by choosing a suitable x value because that's how you'd make it look like 710.
3. (Original post by SeanFM)
You have to work it out from what you've expanded and how you can choose x so that it looks like what you're trying to calculate. (Notice that 1/81 looks like a square number).

In some expansions you can find the number directly, other times (eg you've expanded (8-0.1x)^(1/2) and you want to find the square root of 710, you find 10 * sqrt 7.1 by choosing a suitable x value because that's how you'd make it look like 710.
yeah i know the rough idea how it should be done but don't know how to start basically, should i play around with square root of 1/80 till i get in the form of (8+3x)^1/2?
4. (Original post by Alen.m)
yeah i know the rough idea how it should be done but don't know how to start basically, should i play around with square root of 1/80 till i get in the form of (8+3x)^1/2?
It's 1/81 which is rather important, and the expansion is ^(-2/3), which is also important. Have a think about cube root(1/81) and how you can make it look like (8+3x)^(-2/3), given that a cube root function is already in place.
5. (Original post by SeanFM)
It's 1/81 which is rather important, and the expansion is ^(-2/3), which is also important. Have a think about cube root(1/81) and how you can make it look like (8+3x)^(-2/3), given that a cube root function is already in place.
cube root of 1/81 would be 0.23(to two decimal places) and then should i write it as 23/100 and take it from there? or I'm already going down a wrong path?
6. (Original post by Alen.m)
cube root of 1/81 would be 0.23(to two decimal places) and then should i write it as 23/100 and take it from there? or I'm already going down a wrong path?
You need to use the expansion that you have calculated, rather than a calculator. A calculator is a good way of checking.

Here is another hint... how would you expess cube root(1/81) as something to the power ^(-2/3)?

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