Question

√X - 1/√x if x = 3+2√2

Answer 1

it can also be written as
$given \: x = 3 + 2 \sqrt{2} \\ it \: can \ \:also \: be \: written \: \: as\:$
x= 2+1+2√2
ie x= (√2)²+1²+2√2(1)

Using identity (a+b)²= a²+b²+2ab

we can solve it easily ,

Now x= (√2+1)²
and √x= √(√2+1)²
i.e √x= √2+1

Then 1/√x= 1/√2+1

on rationalizing it we get

= [1/√2+1]× √2-1/√2-1
= √2-1

Now According to the question

√x-1/√x= √2+1-(√2-1
= √2+1-√2+1
= 2

Hope this helps you......✌^_^