Question

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:

\[\sqrt{x} - \frac{1}{\sqrt{x}} = \]

Answer 1

It will take time so you guys can do other work..
I am just writing..

Answer 2

I'm writing too.

Answer 3

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:
\[\sqrt{x} - \frac{1}{\sqrt{x}} = \sqrt{4} = 2\]

Answer 4

but sq. root can have both + and - ve values right ?

Answer 5

Yeah right..
But I am not asking about the answer but the solution..
and of course you are right in that..

Answer 6

Is there any other method simpler than this??

Answer 7

Nah, this is he simplest method in the sense, that it's the least calculative and the most tactical. Nice solution there.

Answer 8

a better one ii think

Answer 9

i just calculated sqrt x

and solved

is it the smartest one

Answer 10

:)

Answer 11

Oh no, I didn't notice that \(3+2\sqrt2\) thingy, it's popular.

Hmm, it IS the smartest procedure Vishwesh, good one!

Answer 12

Thanks

@apoorvk

Answer 13

Yes this is the best.. @vishweshshrimali5

Answer 14

@waterineyes
thanks

Answer 15

Thanks for what???
Even, I should say thanks to you..
Thanks @vishweshshrimali5

Answer 16

:)

Answer 17

Yeah don't thank us Vishwesh, we should thank you for that brilliant work ;)

Answer 18

:)

Answer 19

thanks a lot every one for compliments :D gr8 work @vishweshshrimali5

Answer 20

:)

Answer 21

This is called Quality Solution to this problem..

Answer 22

thanks again :)