Introduction:
Given x = 3 - 2√2, we need to find the value of x 1/x. To solve this, we will first find the value of 1/x and then multiply it with x to get the final result.

Calculating 1/x:
To find the value of 1/x, we need to take the reciprocal of x, which means we need to divide 1 by x.

1/x = 1 / (3 - 2√2)

Rationalizing the denominator:
We can simplify the expression by rationalizing the denominator. To do this, we multiply the numerator and denominator by the conjugate of the denominator, which in this case is (3 + 2√2).

(1 / (3 - 2√2)) * ((3 + 2√2) / (3 + 2√2))
= (3 + 2√2) / ((3 - 2√2) * (3 + 2√2))

Expanding the denominator:
To simplify the expression further, we need to expand the denominator using the distributive property.

= (3 + 2√2) / (9 - (2√2)^2)
= (3 + 2√2) / (9 - 4*2)
= (3 + 2√2) / (9 - 8)
= (3 + 2√2) / 1
= 3 + 2√2

Multiplying with x:
Now that we have found the value of 1/x as 3 + 2√2, we can multiply it with x to get the final result.

x * (3 + 2√2) = (3 - 2√2) * (3 + 2√2)

Using the difference of squares formula:
The expression (a + b)(a - b) is equal to a^2 - b^2. We can apply this formula to simplify the multiplication.

= (3^2 - (2√2)^2)
= (9 - 4*2)
= (9 - 8)
= 1

Final Result:
Therefore, the value of x 1/x is 1.