ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: naved_s9994 on November 05, 2009, 11:51:06 am

Title: How
Post by: naved_s9994 on November 05, 2009, 11:51:06 am: how do you go from the first to last line.
I seriously have forgot! :-[
Title: Re: How
Post by: GerrySly on November 05, 2009, 11:57:34 am: $\begin{align*} \frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-1&=\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-\frac{\sqrt{2}}{\sqrt{2}}\\ &=\frac{1+1-\sqrt{2}}{\sqrt{2}}\\ &=\frac{2-\sqrt{2}}{\sqrt{2}}\\ &=\frac{2-\sqrt{2}}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}\\ &=\frac{2\sqrt{2}-2}{2}\\ &=\frac{2(\sqrt{2}-1)}{2}\\ &=\sqrt{2}-1 \end{align*}$

Put in absolutely everything I could think of heh
Title: Re: How
Post by: StringFever on November 05, 2009, 11:58:35 am: Step 1: Make "1 = root2/root2"
Step 2: Rationalise denominator (so multiply by root 2) - so you get: rt2/2 + rt2/2 - 2/2
Step 3: Simplify, so you have (2rt2)-2/2
Step 4: Take out common factor, so you get: 2 (rt 2 - 1)/2
Step 5: Simplify (cancel 2s)

And voila, there you have it! :)
Title: Re: How
Post by: StringFever on November 05, 2009, 11:59:00 am: Quote from: GerrySly on November 05, 2009, 11:57:34 am
$\begin{align*} \frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-1&=\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-\frac{\sqrt{2}}{\sqrt{2}}\\ &=\frac{1+1-\sqrt{2}}{\sqrt{2}}\\ &=\sqrt{2-\sqrt{2}}{\sqrt{2}}\\ &=\frac{2-\sqrt{2}}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}\\ &=\frac{2\sqrt{2}-2}{2}\\ &=\frac{2(\sqrt{2}-1)}{2}\\ &=\sqrt{2}-1 \end{align*}$

Put in absolutely everything I could think of heh

Dammit, beat me to the chase! :)
Title: Re: How
Post by: ross huggard on November 05, 2009, 12:00:49 pm: not necessary^^
just rationalise the denominators so you get root2/2 + root2/2 which = root2
Title: Re: How
Post by: StringFever on November 05, 2009, 12:02:28 pm: Quote from: ross huggard on November 05, 2009, 12:00:49 pm
not necessary^^
just rationalise the denominators so you get root2/2 + root2/2 which = root2

A little bit of extra working out doesn't hurt :P
Especially if you're prone to careless mistakes like me! :)
Title: Re: How
Post by: simpak on November 05, 2009, 12:27:46 pm: I suck at this most.