A simple Binomial expansion question

**JeWiSh** · March 2nd 2009, 12:15 PM

For the first parts of the question I had to expand $(1+8x)^\frac{1}{2} = 1+4x-8x^2$ and $(1-4x)^\frac{1}{2} = 1+2x+6x^2$

The next part is to find $\sqrt{(1+8x)/(1-4x)}$
I can't get anywhere near the answer in the book, having tried dividing/multiplying the two expansions...

**Prove It** · March 2nd 2009, 12:41 PM

Originally Posted by JeWiSh

For the first parts of the question I had to expand $(1+8x)^\frac{1}{2} = 1+4x-8x^2$ and $(1-4x)^\frac{1}{2} = 1+2x+6x^2$

The next part is to find $\sqrt{(1+8x)/(1-4x)}$
I can't get anywhere near the answer in the book, having tried dividing/multiplying the two expansions...

Those expansions are nonsense.

**JeWiSh** · March 2nd 2009, 01:18 PM

Originally Posted by Prove It

Those expansions are nonsense.

They are? They're just approximations, up to the $x^2$ term. The book says they're right...

**mr fantastic** · March 2nd 2009, 05:39 PM

Originally Posted by JeWiSh

They are? They're just approximations, up to the $x^2$ term. The book says they're right...

You should have said that when you used them.

**JeWiSh** · March 2nd 2009, 11:19 PM

Originally Posted by mr fantastic

You should have said that when you used them.

Sorry...can anyone get me started?

**mr fantastic** · March 3rd 2009, 02:15 AM

Originally Posted by JeWiSh

For the first parts of the question I had to expand $(1+8x)^\frac{1}{2} = 1+4x-8x^2$ and $(1-4x)^\frac{1}{2} = 1+2x+6x^2$

The next part is to find $\sqrt{(1+8x)/(1-4x)}$
I can't get anywhere near the answer in the book, having tried dividing/multiplying the two expansions...

You mean find an approximate expression for $\sqrt{(1+8x)/(1-4x)}$ , right .... ? To what degree?

**JeWiSh** · March 3rd 2009, 03:06 AM

Originally Posted by mr fantastic

You mean find an approximate expression for $\sqrt{(1+8x)/(1-4x)}$ , right .... ? To what degree?

To the $x^2$ term I think, since that's what I was supposed to expand the original expressions to.

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