Please check this... Have I done it right?? Can anybody suggest any other method to solve this: If \(x = 3 + 2\sqrt{2}\) Then, find: \[\sqrt{x} - \frac{1}{\sqrt{x}} = \]
It will take time so you guys can do other work.. I am just writing..
I'm writing too.
Given: \(x = 3 + 2 \sqrt{2}\) I have just did like this: Squaring it: \[(\sqrt{x} - \frac{1}{\sqrt{x} })^2 = x + \frac{1}{x} - 2\] \[= \frac{x^2 + 1 - 2x}{x} = \frac{(x-1)^2}{x}\] Now : \[(x - 1) = 2 + 2\sqrt{2}\] \[(x-1)^2 = 12 + 8\sqrt{2}\] Put in the expression above: \[= \frac{12 + 8\sqrt{2}}{3 + 2\sqrt{2}} = \frac{12 + 8\sqrt{2}}{3 + 2\sqrt{2}} \times \frac{(3 - 2\sqrt{2})}{(3 - 2\sqrt{2})}\] \[= 36 - 24\cancel{\sqrt{2}} + \cancel{24\sqrt{2}} - 32 = 4\] Taking square root both the sides: \[\sqrt{x} - \frac{1}{\sqrt{x}} = \sqrt{4} = 2\]
but sq. root can have both + and - ve values right ?
Yeah right.. But I am not asking about the answer but the solution.. and of course you are right in that..
Is there any other method simpler than this??
Nah, this is he simplest method in the sense, that it's the least calculative and the most tactical. Nice solution there.
a better one ii think
i just calculated sqrt x and solved is it the smartest one
:)
Oh no, I didn't notice that \(3+2\sqrt2\) thingy, it's popular. Hmm, it IS the smartest procedure Vishwesh, good one!
Thanks @apoorvk
Yes this is the best.. @vishweshshrimali5
@waterineyes thanks
Thanks for what??? Even, I should say thanks to you.. Thanks @vishweshshrimali5
:)
Yeah don't thank us Vishwesh, we should thank you for that brilliant work ;)
:)
thanks a lot every one for compliments :D gr8 work @vishweshshrimali5
:)
This is called Quality Solution to this problem..
thanks again :)
|dw:1341768764655:dw|
Join our real-time social learning platform and learn together with your friends!