Author Topic: How (Read 945 times) Tweet Share

naved_s9994 · « **on:** November 05, 2009, 11:51:06 am »

how do you go from the first to last line.
I seriously have forgot!

GerrySly · « **Reply #1 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

StringFever · « **Reply #2 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!

StringFever · « **Reply #3 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!

ross huggard · « **Reply #4 on:** November 05, 2009, 12:00:49 pm »

not necessary^^
just rationalise the denominators so you get root2/2 + root2/2 which = root2

StringFever · « **Reply #5 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

Especially if you're prone to careless mistakes like me!

simpak · « **Reply #6 on:** November 05, 2009, 12:27:46 pm »

I suck at this most.

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