anonymous
  • anonymous
How do I simplify √2-1 / √2 + 1? The answer is 3-2√2. But I got 1.. D:
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
I tried: √2 - 1 √2-1 √2 - 1 ------ = ----- x ------ √2 + 1 √2 + 1 √2 - 1
anonymous
  • anonymous
can u be clear \[\frac{\sqrt{2-1}}{\sqrt{2+1}}\] use conjugates \[\huge{\frac{\sqrt{2-1}}{\sqrt{2+1}}*\frac{\sqrt{2-1}}{\sqrt{2-1}} = \frac{(2-1)}{\sqrt{3}} = \frac{1}{\sqrt{3}}}\]
anonymous
  • anonymous
no it's just: √2 - 1 / √2 + 1

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anonymous
  • anonymous
\[\huge\frac{\sqrt{2-1}}{\sqrt{2-1}}=1\]
Mimi_x3
  • Mimi_x3
\[\large \frac{\sqrt{2}-1}{\sqrt{2}+1} *\frac{\sqrt{2}-1}{\sqrt{2}-1} = \frac{(\sqrt{2}-1)(\sqrt{2}-1)}{2-1} = \frac{3-2\sqrt{2}}{1} =3-2\sqrt{2} \]
anonymous
  • anonymous
why is the denominator: 2-1?
anonymous
  • anonymous
and the denominator: 3 - 2√2?
EscherichiaRinku
  • EscherichiaRinku
(a+b)(a-b)=a^2+b^2
anonymous
  • anonymous
ohh..
EscherichiaRinku
  • EscherichiaRinku
and the nominator is (a-b)(a-b) = (a-b)^2 expanded into a^2-2ab+b^2
Mimi_x3
  • Mimi_x3
because \((\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b}) = a - b\)
anonymous
  • anonymous
ohh, thank you! I have to memorize those right?
Mimi_x3
  • Mimi_x3
hm..if you want to lol. You can use FOIL to work it out anyway, might be harder; depends on you xD
anonymous
  • anonymous
ohh, i see.
EscherichiaRinku
  • EscherichiaRinku
At school we were all forced to memorize such formulas, lol. Well, if you work on enough problems the simplification formulas will be intuitive :D
anonymous
  • anonymous
ohh, thanks guys!
anonymous
  • anonymous
Mimi, how did you get 3 - 2√2/1? D:
anonymous
  • anonymous
'cause don't I have to multiply: √2*√2*√2*-1?
Mimi_x3
  • Mimi_x3
I used FOIL, to do it. Or you can use \[(\sqrt{a}-\sqrt{b})^{2} = a-2\sqrt{ab} +b\] I don't know what you are doing there, sorry.

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