Question

if x=3+2 root 2 ten how 1/x=3-2 root 2

Answer 1

You rationalize it.
x= 3+2√2
1/x= 1/3+2√2
= 1/3+2√2 × 3-2√2/3-2√2
= 3-2√2/ (3)^2 - (2√2)^2
= 3-2√2/ 9 - 8
= 3-2√2/1 = 3-2√2

It's as simple as that, friend.

Answer 2

In the question it is given that x= 3+2√2
1/x = 1/3+2√2
By rationalising the denominator we get,
1/x = [(1)× 3-2√2] / [3+2√2× 3-2√2]

1/x = ( 3-2√2)/[3²-(2√2)²] { because a²-b² = (a+b)(a-b)}

1/x = (3-2√2)/(9-8)

1/x = (3-2√2)

Hope this helps you